
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
Given \( P(x) = x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 \) which satisfies \( P(k) = k \) for \( k = 1, 2, 3, 4 \), find \( \sqrt{P(13) - 12} = \quad \) .

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