Coin With a Random Bias

A wheel picks $X \sim$ Uniform(0,1). You then flip a coin 12 times, each flip landing heads with probability $X$, with the same $X$ held fixed for all 12 flips. Let $Y$ be the number of heads.

What is $P(4 \leq Y \leq 6)$?

Answer format: round to 3 decimal places.