
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
Consider integers \( S_k \) analogously defined like \( R_k \) such that \( S_k \) represents \( k \)-length sequence of twos in its decimal presentation (for instance, \( S_3 = 222 \)). Determine the number of zeros in the quotient when \( S_{30} \) is divided by \( S_5 \).
A) 16
B) 18
C) 20
D) 22
E) 24

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