
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 △ABC, it is known that 2B = A + C and c = 2a.
1. Find the measures of angles A, B, and C.
2. Let the sequence {a\_n} satisfy a\_n = n|cos(nC)|, and the sum of the first n terms is S\_n. If S\_n = 20, find the value of n.

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