
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 with any digit from $0,1,2,3,4,5,6,7,8$ (digits may repeat) in such a way that the resulting 12-digit number is divisible by 45. How many ways can this be done?

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