
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
Expand $(x^2 - x - 1)^n$ to get $a_{2n}x^{2n} + a_{2n-1}x^{2n-1} + \ldots + a_2x^2 + a_1x + a_0$, and find the value of $a_0 + a_2 + a_4 + \ldots + a_{2n}$.

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