
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 \( P(x) \) be a polynomial with integer coefficients such that \( P(-4) = 5 \) and \( P(5) = -4 \). What is the maximum possible remainder when \( P(0) \) is divided by 60?

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