
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 $(1 - x + x^2)^n = b_0 + b_1 x + b_2 x^2 + \cdots + b_{2n} x^{2n}$ be an identity in x. Calculate the sum $t = b_0 + b_2 + b_4 + \cdots + b_{2n}$.

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