
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
In the triangle  $ABC$  on the sides  $AB$  and  $AC$  outward constructed equilateral triangles  $ABD$  and  $ACE$ . The segments  $CD$  and  $BE$  intersect at point  $F$ . It turns out that point  $A$  is the center of the circle inscribed in triangle  $ DEF$ . Find the angle  $BAC$ .

(Rozhkova Maria)

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