
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 with $DE = EF$ and side $DF = 40$ units. The incenter of $\triangle DEF$ is $J$, and the distance from $J$ to side $DF$ is $25$ units. What is the length of the inradius of $\triangle DEF$?

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