
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 $ABC$, $AB = 8$, $AC = 17$, and $BC = 15$. The medians $AD$, $BE$, and $CF$ intersect at the centroid $G$. The centroid divides the median into the ratio $2:1$ with the longer segment being from the vertex to the centroid. Let $P$ be the foot of the altitude from $G$ to side $BC$. Find the length of segment $GP$.

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