
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 $g(13)=40$, and if there exists an integer $a$ such that $g(a)=b$, then $g(b)$ is defined and:

$g(b)=3b+5$ 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}
user