
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
Suppose \( z^{2022} + 1 = (z^2 + z + 1)S(z) + T(z) \), where \( S(z) \) and \( T(z) \) are polynomials and the degree of \( T(z) \) is less than 2, determine the polynomial \( T(z) \).

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