
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
Let \( P(z) \) and \( S(z) \) be the unique polynomials such that \[ z^{2023}+1 = (z^2+z+1)P(z) + S(z) \] and the degree of \( S \) is less than 2. What is \( S(z)? \)
A) z
B) -1
C) z + 1
D) 2023
E) 2z + 1

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