
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 \( f(x) = 4x^4 + 12x^3 - 9x^2 + x + 3 \) and \( d(x) = x^2 + 4x - 2 \). If \( f(x) = q(x)d(x) + r(x) \) for some polynomials \( q(x) \) and \( r(x) \) where \( \deg r < \deg d \), calculate \( q(1) + r(-1) \).

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