
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
For polynomial $R(x) = 1 - \frac{1}{4}x + \frac{1}{8}x^3$, define
\[S(x) = R(x)R(x^2)R(x^4)R(x^6)R(x^8)R(x^{10}) = \sum_{i=0}^{60} b_ix^i.\]
Find $\sum_{i=0}^{60} |b_i|$.

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