
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$  be an isosceles triangle with  $ AB\equal{}AC$ , and  $ D$  be midpoint of  $ BC$ , and  $ E$  be foot of altitude from  $ C$ . Let  $ H$  be orthocenter of  $ ABC$  and  $ N$  be midpoint of  $ CE$ .  $ AN$  intersects with circumcircle of triangle  $ ABC$  at  $ K$ . The tangent from  $ C$  to circumcircle of  $ ABC$  intersects with  $ AD$  at  $ F$ .
Suppose that radical axis of circumcircles of  $ CHA$  and  $ CKF$  is  $ BC$ . Find  $ \angle BAC$ .

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