
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Equilateral triangle $XYZ$ has a side length of 8, and a circle inscribed in this triangle touches side $XY$ at point $C$. A right triangle $ABC$ (hypotenuse $\overline{AB}$) is inscribed in triangle $XYZ$ such that point $C$ is also a vertex of triangle $ABC$. If $XC = 2$ and $CY = 3$, compute the length of $AQ$, where $A$ is on $YZ$ and $B$ on $XZ$.

Present the answer in LaTex format: \boxed{Your answer}
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