
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 \(ABCD\) be a square of side length 13. Let \(E\) and \(F\) be points on rays \(AB\) and \(AD\), respectively, so that the area of square \(ABCD\) equals the area of triangle \(AEF\). If \(EF\) intersects \(BC\) at \(X\) and \(BX = 6\), determine \(DF\).

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