I have a rifle marked Premier Trailblazer with an octagon barrel.
I think it was made by Stevens or Savage.
It looks like a Savage model 29 .22 S/L/LR rifle.

The barrel seems to be a little loose in the receiver.
It looks like it kind of pivots around the barrel pin that goes through the receiver.

Is there some way to tighten this up?
In some other threads, I saw comments about a barrel nut.
Does this model have a barrel nut that could have become loose?
If so, can I tighten up this nut without taking out the barrel pin?

Would it be safe to shoot this rifle with this looseness?

Any help and/or advice would be appreciated.