
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
Zan has modified his iterative rule for generating sequences of whole numbers:

1) If a number is 25 or less, triple the number.
2) If a number is greater than 25, subtract 15 from it.

Define $F$ as the first number in a sequence generated by the new rules. $F$ is a "sweet number" if 18 is not a term in the sequence that starts with $F$. Determine how many of the whole numbers 1 through 50 are "sweet numbers"?

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