
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
For each positive integer \( n \), define \( s(n) \) to equal the sum of the digits of \( n \). For example, \( s(2023)=2+0+2+3 \). The number of integers \( n \) with \( 100 \leq n \leq 999 \) and \( 7 \leq s(n) \leq 11 \) is \( S \). What is the integer formed by the rightmost two digits of \( S \)?

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