
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
Triangle $XYZ$ has sides $XY = 15$, $XZ = 17$, and $YZ = 8$. Points $P$ and $Q$ are located on $\overline{XY}$ and $\overline{XZ}$, respectively, such that $\overline{PQ}$ is parallel to $\overline{YZ}$ and goes through the midpoint of $\overline{YZ}$. Calculate $PQ$.

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