
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 \( q(x) = x^{10} + x^9 + x^8 + \cdots + x + 1 \), and let \( s(x) \) be the polynomial remainder when \( q(x) \) is divided by \( x^3 + x^2 + 1 \). Find the remainder when \( |s(10)| \) is divided by \( 100 \).

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