
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
Medians $\overline{DP}$, $\overline{EQ}$, and $\overline{FR}$ of $\triangle DEF$ are such that $\overline{DP}$ and $\overline{EQ}$ are perpendicular, and $\overline{FR}$ is parallel to $\overline{DP}$. If $DP = 15$ and $EQ = 20$, compute the length of ${DF}$.

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