
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 \(Q(z)\) and \(R(z)\) be polynomials such that
\[
z^{2023} + 1 = (z^2 + z + 1)Q(z) + R(z)
\]
and the degree of \(R\) is less than 2. Find the polynomial \(R(z)\).
A) \( -z + 1 \)
B) \( z + 1 \)
C) \( -z \)
D) \( 1 \)
E) \( z \)

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