
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
Given the set $A=\{-1,-\frac{1}{2},-\frac{1}{3},0,\frac{2}{3},2,3\}$, $B=\{y=f\left(x\right)|f\left(x\right)=x^{k}$, $k\in A$ and the graph of $y=f\left(x\right)$ is symmetric about the $y$-axis$\}$, then the number of elements in set $B$ is ______.

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