
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

A polynomial \( P(x) \) of degree 10 with a leading coefficient of 1 is given. The graph of \( y = P(x) \) lies entirely above the x-axis. The polynomial \( -P(x) \) was factored into irreducible factors (i.e., polynomials that cannot be represented as the product of two non-constant polynomials). It is known that at \( x = 2020 \), all the resulting irreducible polynomials take the value -3. Find \( P(2020) \).

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