
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 a, b, and c, respectively. Given the equation 3acosA = ccosB + bcosC,

1. Find the value of cosA.
2. If a = $2\sqrt{3}$ and cosB + cosC = $\frac{2\sqrt{3}}{3}$, find the length of side c.

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