
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 the polynomial
\[ f(x)=x^{2020}+\sum_{i=0}^{2019} c_{i} x^{i} \quad (c_{i} \in\{-1,0,1\}), \]
let \( N \) be the number of positive integer roots of \( f(x) \), including their multiplicities. If the equation \( f(x) = 0 \) has no negative integer roots, determine the maximum value of \( N \).

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