
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 of the form \( a_0 + a_1x + \cdots + a_nx^n \), where \(a_0, a_1, \ldots, a_n\) are integers (including negative values). Find the number of such polynomials where the sum of the absolute values of the coefficients plus the polynomial degree equals 4.
A) 5
B) 6
C) 10
D) 15

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