
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 $P(x)=b_0+b_1x+\dots+b_nx^n$ be a polynomial with integer coefficients, and $0\le b_i<4$ for all $0\le i\le n$.

Given that $P(\sqrt{3})=30+25\sqrt{3}$, compute $P(3)$.

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