
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
Each of the integers \(1, 2, \ldots, 729\) is written in its base-3 representation without leading zeroes. The numbers are then joined together in that order to form a continuous string of digits. How many times in this string does the substring 012 appear?

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