
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
Suppose we define a function $g(x)$ such that $g(21) = 46$, and if there exists an integer $c$ such that $g(c) = d$, then $g(d)$ is defined and follows these rules:

\[g(d) = 2d + 2 \quad \text{if } d \text{ is even}\]

\[g(d) =\frac{d - 1}{2} \quad \text{if } d \text{ is odd}\]

What is the smallest possible number of integers in the domain of $g$?

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