
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
\[ y^8 - 50y^4 + 25 = a(y) b(y) \]
where $a(y)$ and $b(y)$ are monic, non-constant polynomials with integer coefficients. Find $a(1) + b(1)$.

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