
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 \( P(x) = x^4 + a x^3 + b x^2 + c x + d \), where \( a, b, c, d \) are constants, and \( P(1) = 2000 \), \( P(2) = 4000 \), \( P(3) = 6000 \), find \( P(9) + P(-5) \).

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