
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 \( b_{20} = 20 \), and for each positive integer \( n > 20 \) let \( b_n = 200b_{n-1} - n \). Find the least positive \( n > 20 \) such that \( b_n \) is a multiple of 121.

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