
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 \( f(x) = (1 + x^2 + x^4)^n \). Expanding \( f(x) \) results in a polynomial 
\[ f(x) = b_0 + b_1x + b_2x^2 + \cdots + b_{4n}x^{4n}. \]
Compute the value of \( s = b_0 + b_4 + b_8 + \cdots + b_{4n} \).

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