Need help identifying my new Longines!

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Can anyone help me identify my new Longines without the reference number? I was told it is a 1950's era watch. It is approximately 37 mm from my measurement. Any help would be greatly appreciated!
 
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296
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550
Oh wow is it refinished!? I had no idea. I did not pay much, but I don't think I would've purchased it at all knowing it is refinished. Thanks though.