
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 that 2(tanA + tanB) = $\frac{\text{tanA}}{\text{cosB}} + \frac{\text{tanB}}{\text{cosA}}$.
(1) Find the value of $\frac{a+b}{c}$;
(2) If c = 2 and C = $\frac{\pi}{3}$, find the area of triangle ABC.

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