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Houston (CNN) Nick Tullier's family never stopped dreaming of the day the East Baton Rouge, Louisiana, sheriff's deputy would emerge from a coma. That day finally arrived.

"People have asked us a number of times, 'Is Nick a miracle?'" said James Tullier, Nick's father, as he grinned.

"To us, yes. Nick's a miracle."

Since July 17, when he was shot in the head and abdomen after answering a call to take down an active shooter who was targeting officers, the family of Nick Tullier hasn't left his side.

Tullier spent four months in a coma and has spent the last month going through intense rehabilitation at TIRR Memorial Hermann in Houston. His parents and fiancée have been working with him on an extremely difficult, yet astounding recovery.

Nick Tullier goes through hours of physical, occupational, speech and neurological therapy each day.

'The place where miracles happen'

On November 16, with a series of medical setbacks in the rear-view mirror, they were finally able to move Tullier to TIRR Memorial Hermann, a move they were optimistic about.

"We heard from many people -- this is the place where miracles happen," James Tullier said at a December 15 press conference.

Doctors at TIRR Memorial Hermann say shortly after his arrival, they quickly found that Tullier was conscious and completely aware of different aspects of his environment.

"We've identified that Nick can see, Nick can hear," Katherine O'Brien, a clinical neuropsychologist at TIRR Memorial Hermann, said at the press conference.

"Nick understands language. Nick knows who he is, Nick knows where he is. He can identify that he is in Houston, Texas, and in a hospital. Nick can identify his family members. Nick can communicate with a nonverbal yes, no system. He can read words, both simple and syllabic. And he can follow commands."

Doctors say that Tullier still has "severe weakness" throughout his body, and that his muscles feel very tight and rigid, limiting his movement.

Tullier can move his left hand, arm.

He communicates by nodding forward for "yes" and turning to the right for "no," controlling the movements himself as staff help him hold his head muscles up.

Tullier is able to move his left hand, and his arm, and he is able to have some movement in his legs. He can write his initials, with TIRR Memorial Hermann staff helping to support his arm.

He is out of bed every day, working hard through at least three to four hours of physical, occupational, speech, and neurological therapy.

"Nick's recovery has been surprising," said Dr. Sunil Kothari, medical director of the Disorders of Consciousness Program at TIRR Memorial Hermann.

"While it's still very early in this phase of Nick's rehabilitation, I'd say he's much further along than we would have expected, based on what we knew before his arrival."

Nick Tullier can write his initials.

A family's hope

After the shooting, Tullier's heart stopped four times in the first 24 hours he was in the emergency room.

James Tullier says doctors told the family that his son would not live another day, but he continued to defy the odds and expectations at every turn.

It was sporadic progress, but since the first week, he's been able to breathe on his own, without help from a machine.

The first breakthrough happened in August, when Tullier's family realized he was wiggling his toes. And for a brief time, they said, Tullier slowly and deliberately moved his toes and gently squeezed their hand. It was one of the most emotional moments of this long ordeal.

The family allowed CNN to visit them in September, in the hospital room where Tullier, 41, was still undergoing surgeries and treatments to save his life.

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Danielle McNicoll, Nick Tullier's fiancé, told CNN that the two were planning to get married next summer.

While he was in a coma, McNicoll would frequently ask Tullier to stick his tongue out at her, and she says many times he was able to do it.

"You can definitely tell that he can hear when we are talking to him. A lot of times he'll open his right eye, he moved his head, he moved his toes. He's there. It takes a lot out of him," McNicoll told CNN in September. "Medically, he should not be here, and he is."

Mary Tullier, Nick Tullier's mother, leaned over her son's head in the hospital bed and whispered, "I know you can hear me." Her finger caressed his forearm as she whispered again, "I know you can hear me."

"We were told he could never communicate ever again. And he can communicate," James Tullier said.

"You can see in his face at times that he's wanting to talk to us. Because he gets a frustrated look after a period of time when you know, you are talking to him, and he's wanting to communicate back. And at times you can even see him kinda tense up his arms," he said.

"But it's going to come in time. I mean look at what he's done so far in this short period of time. We know he understand us. He has understood what has been said around him for a long time. But it's just a miracle every day."

Nick Tullier spent four months in a coma.

The shooting and race to the hospital

On a quiet Sunday morning in July, a lone gunman ambushed officers on the streets of Baton Rouge.

Nick Tullier and two other East Baton Rouge Sheriff's deputies were sipping coffee at Frank's Restaurant, their regular Sunday morning haunt beloved by locals for down-home Cajun cooking.

Then the call came over the radio from just down the road on Airline Highway, and they instantly recognized the voice. It was Deputy Brad Garafola, one of the three law enforcement officers who was eventually killed by Gavin Long that morning.

The officers raced to the shooting scene down the road. Nick Tullier was the first to arrive. James Tullier says his son never saw the gunman, who emerged from the woods just off the road, and he never had a chance to defend himself.

The gunman fired one round into Nick Tullier's head. The bullet lodged in the back of his head and, according to his family, has caused severe brain stem damage.

Tullier was then shot twice in the abdomen and has undergone more than 12 surgeries to repair the internal damage to his organs.

"That guy that did the shooting was pure evil," Tullier said. "Came here on a vengeance with a mission in mind. It was just to kill police officers."

Van Foster, an investigator with the East Baton Rouge District Attorney's Office, has been close friends with Nick Tullier since their high school football days in Denham Springs. He isn't surprised Tullier raced into the active shooting scene.

"His moral compass is always pointing due north," Foster said. "I guarantee you the thought in his mind is there were officers down and there were potential people in danger."

First responders raced Tullier to the hospital and his family was told to arrive at the hospital quickly because his chances of surviving were slipping away.

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"It's in his head. He's the fighter," James Tullier said, adding that before the shooting, Nick Tullier said he was in the best shape of his life. "He's the strong, and he's pushing. He's pushing through hurts, that's what he's done in life. And it's just amazing to see what they have accomplished with him and it's amazing to see what Nick has accomplished."

"We know he's going to face challenges. No one recovers from this severe of a brain injury completely," Dr. Kothari said at the press conference earlier this month. "The question is how challenged will they be? Both from a cognitive thinking point of view and a physical point of view."

James Tullier and the family understand that Nick Tullier has a long road ahead, but they remain optimistic about the possibilities and thankful for where they are.

"What's in Nick's future? I mean look at what had been in Nick's past," James Tullier said. "We had no hope. Nick wasn't supposed to survive one day. Two days. Five days. Three weeks. Look where he is at."