
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
Given a polynomial of the form $a_0x^n + a_1x^{n-1} + ... + a_n$, find how many such polynomials exist where twice the sum of the absolute values of the coefficients plus the degree of the polynomial equals 4.
A) 2
B) 3
C) 4
D) 5

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