
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 $DEF$, $DE = 10$, $DF = 15$, and $EF = 17$. The medians $DM$, $EN$, and $FO$ of triangle $DEF$ intersect at the centroid $G$. Let $P$ be the foot of the altitude from $G$ to $EF$. Calculate the length of $GP$.

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