
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
Define a function \( f(x) \) such that \( f(15) = 22 \), and if there exists an integer \( a \) such that \( f(a) = b \), then \( f(b) \) is defined and follows these rules:
- \( f(b) = 3b + 1 \) if \( b \) is odd
- \( f(b) = \frac{b}{2} \) if \( b \) is even.

What is the smallest possible number of integers in the domain of \( f \)?

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