
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
Ali has formulated a new rule for creating sequences of integers:

1) If a number is 20 or less, triple the number.

2) If the number is greater than 20, subtract 15 from it.

Let $G$ be the initial number in a sequence generated by Ali's rule. $G$ is a "golden number" if 12 is not a term in the sequence that begins with $G$. Determine how many integers from 1 to 40 are "golden numbers."

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