
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
A circle passes through vertex \( B \) of the triangle \( ABC \), intersects its sides \( AB \) and \( BC \) at points \( K \) and \( L \), respectively, and touches the side \( AC \) at its midpoint \( M \). The point \( N \) on the \(\operatorname{arc} BL\) (which does not contain \( K \)) is such that \(\angle LKN = \angle ACB\). Find \(\angle BAC\) given that the triangle \( CKN \) is equilateral.

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