
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
The inscribed circle of triangle $DEF$ is tangent to side $\overline{DE}$ at point $M$, and its radius is $15$. Given that $DM=17$ and $ME=39$, calculate the area of triangle $DEF$. Additionally, find the length of the median from $D$ to side $\overline{EF}$.

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