
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 \( P(x) = b_0 + b_1 x + \cdots + b_n x^n \) be a polynomial with integer coefficients, where \(0 \leq b_i < 5\) for all \(0 \leq i \leq n\).

Given that \(P(\sqrt{5}) = 40 + 30\sqrt{5}\), compute \(P(3)\).

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