
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  $f(x)=x^{2020}+\sum_{i=0}^{2019} c_ix^i$ , where  $c_i \in \{ -1,0,1 \}$ . Denote  $N$  the number of positive integer roots of  $f(x)=0$  (counting multiplicity). If  $f(x)=0$  has no negative integer roots, find the maximum of  $N$ .

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