
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 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) \( 2z + 1 \)
E) \( z - 1 \)

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