
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
\[y^8 - 32y^4 + 64 = a(y) b(y),\]
where \(a(y)\) and \(b(y)\) are monic, non-constant polynomials with integer coefficients. Find \(a(2) + b(2)\).

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