
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 $f(7)=22$, and if an integer $a$ satisfies $f(a)=b$, 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}
user