
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
Find the number of polynomials of the form $a_0x^n + a_1x^{n-1} + \cdots + a_{n-1}x + a_n$, where all coefficients are integers, the sum of the absolute values of the coefficients plus the degree of the polynomial equals 5, and at least one coefficient must be negative.
A) 3
B) 5
C) 6
D) 7

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