
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  $a_{10} = 10$ , and for each integer  $n >10$  let  $a_n = 100a_{n - 1} + n$ . Find the least  $n > 10$  such that  $a_n$  is a multiple of  $99$ .

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