
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
Given an integer  $n \geq 2$ , determine all  $n$ -digit numbers  $M_0 = \overline{a_1a_2 \cdots a_n} \ (a_i \neq 0, i = 1, 2, . . ., n)$  divisible by the numbers  $M_1 = \overline{a_2a_3 \cdots a_na_1}$  ,   $M_2 = \overline{a_3a_4 \cdots a_na_1 a_2}$ ,  $\cdots$  ,  $M_{n-1} = \overline{a_na_1a_2 . . .a_{n-1}}.$ 

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