
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 $(1-x+x^2)^n = b_0 + b_1x + b_2x^2 + \cdots + b_{2n}x^{2n}$ be an identity in $x$. Calculate $t = b_0 + b_2 + b_4 + \cdots + b_{2n}$.
A) $\frac{2^n + 1}{2}$
B) $\frac{3^n + 1}{2}$
C) $2^n$
D) $\frac{3^n + 2^n}{2}$

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