
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  $ABC$  and  $DEF$  be two triangles, such that  $AB=DE=20$ ,  $BC=EF=13$ , and  $\angle A = \angle D$ . If  $AC-DF=10$ , determine the area of  $\triangle ABC$ .

*Proposed by Lewis Chen*

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