
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, C are a, b, c, respectively. If A, B, C form an arithmetic sequence and c = 2a,

1. Find the measure of angle A.
2. Let the sequence {a\_n} satisfy a\_n = 2^n |cos(nC)|, where S\_n is the sum of the first n terms. If S\_n = 20, find the value of n.

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