
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
Let $\triangle DEF$ be an isosceles triangle such that $DE = EF = 40$ and $DF = 50$. The incenter of the triangle is $J$, and $JF = 26$. Calculate the radius of the incircle of $\triangle DEF$.

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