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Baby, Bruce was born to puuuuuump ... up ... in the only gym he could possibly walk into with his head held high.

Yes, Bruce Springsteen was working on his fitness Monday morning by cruising into a Jersey Strong gym ... 'cause it's only right. As you'd expect from the Boss -- no yoga pants or spandex shirts. Just a white tee, flannel and jeans. He even stopped for photos with a couple fans.