
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  $a_1=24$  and form the sequence  $a_n$ ,  $n\geq 2$  by  $a_n=100a_{n-1}+134$ . The first few terms are  $$ 24,2534,253534,25353534,\ldots $$  What is the least value of  $n$  for which  $a_n$  is divisible by  $99$ ?

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