
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  $\Gamma$  be the circumcircle of a triangle  $ABC$  and let  $E$  and  $F$  be the intersections of the bisectors of  $\angle ABC$  and  $\angle ACB$  with  $\Gamma$ . If  $EF$  is tangent to the incircle  $\gamma$  of  $\triangle ABC$ , then find the value of  $\angle BAC$ .

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