
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
ABC is a triangle with incenter I. M is the midpoint of AC and N is the midpoint of AB. The lines NI and AC meet at X, and the lines MI and AB meet at Y. The triangles AXY and ABC have the same area. Find angle A.

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