
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
Let \((1-x+x^2)^n = a_0 + a_1x + a_2x^2 + \cdots + a_{2n}x^{2n}\) be an identity in \(x\). Define \(s = a_0 + a_2 + a_4 + \cdots + a_{2n}\). What is the value of \(s\)?
A) \( \frac{1 + 3^n}{2} \)
B) \( 3^n \)
C) \( \frac{3^n - 1}{2} \)
D) \( \frac{3^n + 1}{2} \)
E) \( \frac{2^n + 1}{2} \)

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