
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
Determine the coefficients $a$ and $b$ in the polynomial $f(x) = ax^3 - 3x^2 + bx - 7$ such that when $f(x)$ is divided by $x - 2$, the remainder is $-17$, and when divided by $x + 1$, the remainder is $-11$.

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