
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 $a_{20} = 20$, and for each positive integer $n > 20$, define $a_n = 50a_{n-1} + n$. Find the least positive $n > 20$ such that $a_n$ is a multiple of 121.

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