
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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