
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
Consider \( P(x) = \sum_{k=0}^{n} a_{k} x^{k} \in \mathbb{R}[X] \) of degree \( n \). What is \( P^{(j)}(0) \) for \( j \in \mathbb{N} \)?

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