
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 \(P(x) = 1 + \frac{1}{4}x - \frac{1}{8}x^2\), define
\[Q(x) = P(x)P(x^2)P(x^4)P(x^6)P(x^{10}) = \sum_{i=0}^{60} a_ix^{i}.\]
Find \(\sum_{i=0}^{60} |a_i|\).

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