
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 inscribed in triangle \(ABC\) touches sides \(AB\) and \(AC\) at points \(D\) and \(E\) respectively. Point \(I_A\) is the center of the excircle opposite side \(BC\) of triangle \(ABC\). Points \(K\) and \(L\) are the midpoints of segments \(DI_A\) and \(EI_A\) respectively. Lines \(BK\) and \(CL\) intersect at point \(F\) located inside angle \(BAC\). Find \(\angle BFC\), given that \(\angle BAC = 50^\circ\). (The excircle touches side \(BC\) and the extensions of sides \(AB\) and \(AC\) beyond points \(B\) and \(C\) respectively.)

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