
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
In triangle ABC, the sides opposite to angles A, B, and C are denoted as a, b, c, respectively. If (a-2b)cosC = c(2cosB-cosA), and the area of triangle ABC is a<sup>2</sup>sin$\frac{A+B}{2}$, then find the measure of angle C.

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