
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 polynomial \( f(x) = ax^4 + 3x^3 - 5x^2 + bx - 7 \). When \( f(x) \) is divided by \( x - 2 \), the remainder is \( 9 \). When \( f(x) \) is divided by \( x + 1 \), the remainder is \( -4 \). Determine the ordered pair \( (a, b) \).

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