
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
Find the largest integer  $n \ge 3$  for which there is a  $n$ -digit number  $\overline{a_1a_2a_3...a_n}$  with non-zero digits $a_1, a_2$  and  $a_n$ , which is divisible by  $\overline{a_2a_3...a_n}$ .

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