
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
The area of triangle \( ABC \) is 1, \(\angle A = \operatorname{arctg} \frac{3}{4}\), point \( O \) is the midpoint of side \( AC \). A circle centered at point \( O \) is tangent to side \( BC \) and intersects side \( AB \) at points \( M \) and \( N \), with \( AM = NB \). Find the area of the part of triangle \( ABC \) that is inside the circle.

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