
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 $DEF$, we have $DE=2$ and $DF=3$. Side $\overline{EF}$ and the median from $D$ to $\overline{EF}$ have the same length. What is $EF$? Express your answer in simplest radical form.

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