
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 \( P(x) = b_0 + b_1x + \dots + b_mx^m \) be a polynomial with integer coefficients, where \( 0 \leq b_i < 4 \) for all \( 0 \leq i \leq m \).

Given that \( P(\sqrt{2}) = 30 + 26\sqrt{2} \), compute \( P(3) \).

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