
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
For positive integer  $n$  let  $a_n$  be the integer consisting of  $n$  digits of  $9$  followed by the digits  $488$ . For example,  $a_3 = 999,488$  and  $a_7 = 9,999,999,488$ . Find the value of  $n$  so that an is divisible by the highest power of  $2$ .

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