
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
Let k be a positive integer. Find the number of non-negative integers n less than or equal to  $10^k$  satisfying the following conditions:
(i) n is divisible by 3;
(ii) Each decimal digit of n is one of the digits 2,0,1 or 7.

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