
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
In the number $2 * 0 * 1 * 6 * 0 * 2 *$, each of the 6 asterisks must be replaced by any of the digits $0, 2, 4, 5, 7, 9$ (digits can be repeated) so that the resultant 12-digit number is divisible by 75. In how many ways can this be done?

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