
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
In triangle $XYZ$, $XY = 15$, $XZ = 17$, and $YZ = 24$. The medians from vertices $X$, $Y$, and $Z$ intersect at the centroid $G$. Let $Q$ be the foot of the altitude from $G$ to side $XZ$. Find the length of segment $GQ$.

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