
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 cubic polynomial such that
\[ P(x) = P(0) + P(1)x + P(2)x^2 + P(3)x^3 \]
and \( P(-1) = 2 \). Also, it is given that \( P(0) = 3 \). Find \( P(x) \) if \( P(1) = 1 \) and \( P(2) = 15 \).

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