
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
A positive integer is called a "random number" if and only if:
(1) All digits are non-zero.
(2) The number is divisible by 11.
(3) The number is divisible by 12, and if the digits of the number are permuted in any way, the resulting number is still divisible by 12.
How many such ten-digit random numbers are there?

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