
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
An incircle is inscribed in an isosceles triangle \(ABC\) with base \(AC\). The incircle touches the side \(AB\) at point \(M\). From point \(M\), a perpendicular \(ML\) is drawn to side \(AC\). Find the measure of angle \(C\) if the area of triangle \(ABC\) is 1 and the area of quadrilateral \(LMBC\) is \(s\).

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