
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
Consider a modified sequence rule that Zan has created:
1) If a number is 30 or less, triple the number.
2) If a number is more than 30, subtract 15 from it until it falls 30 or less.

Let $G$ be the first number in a sequence. $G$ is a "sweet number" if a term in the sequences formed by $G$ is never equivalent to 18 mod 15. Determine how many of the whole numbers 1 through 60 are "sweet numbers".

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