
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
We define a function \(f(x)\) such that \(f(7)=22\), and if there exists an integer \(a\) such that \(f(a)=b\), then \(f(b)\) is defined and
- \(f(b)=3b+1\) 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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