
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 \(g(x)\) such that \(g(11) = 24\), and if there exists an integer \(a\) such that \(g(a) = b\), then \(g(b)\) is defined and
\[ g(b) = 3b + 1 \] if \(b\) is odd
\[ g(b) = \frac{b}{2} \] if \(b\) is even.
What is the smallest possible number of integers in the domain of \(g\)?

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