
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 \(A B C D\) be a square of side length 13. Let \(E\) and \(F\) be points on rays \(A B\) and \(A D\), respectively, so that the area of square \(A B C D\) equals the area of triangle \(A E F\). If \(E F\) intersects \(B C\) at \(X\) and \(B X = 6\), determine \(D F\).

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