I don't actually know what size it is, but be aware that the 92 Bravado was True Temper and your Avalanche is Tange Prestige so they may well be different.
all early Prestige framed GT's took 27.0mm seat posts...own them all and can confirm that. You can actually buy those old original equipment Tioga Prestige chromoly posts on eBay NOS.
Have purchased a few in the past to keep builds P-E-R-I-O-D correct.
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Thanks gm! Reason for the post is that I had tracked down a 27.2mm tioga post with the correct decal as I had it in my head that was the right size - all the way from Auz and it didn't blooming fit!
Have now bought one from the link you gave, near as damit!