
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
For a natural number, perform the following operation: If it is a multiple of 3, divide it by 3. If it is not a multiple of 3, add 1, and continue this process until the result is 1. If such operations are performed 5 times until it stops, how many starting numbers are there?

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