
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 \( f(x) = x^{2020} + \sum_{i=0}^{2019} c_i x^i \) where \( c_i \in \{-1, 0, 1\} \) for \( 0 \leq i \leq 2019 \). Let \( N \) denote the number of positive integer roots (including multiplicities) of \( f(x) \). If the equation \( f(x) \) has no negative integer roots, find the maximum value of \( N \).

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