
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
Given in triangle $\triangle ABC$, the sides opposite to angles A, B, C are a, b, c respectively, and the area of triangle ABC is $2 \sqrt{3}$, a+b=6, and $\frac{a\cos B+b\cos A}{c} =2\cos C$, calculate the value of c.

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