
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
Consider a monic polynomial $f(x)$ of degree $3$ such that $f(0) = 4$, $f(1) = 10$, and $f(-1) = 2$. Determine $f(x)$ in the form $ax^3+bx^2+cx+d$ where $a$, $b$, $c$, and $d$ are real numbers.

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