
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
8. Andrey likes all numbers that are not divisible by 3, and Tanya likes all numbers that do not contain digits that are divisible by 3.

a) How many four-digit numbers are liked by both Andrey and Tanya?

b) Find the total sum of the digits of all such four-digit numbers.

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