
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 that the function $f(x)$ is defined on $(-\infty,0)\cup(0,+\infty)$ and is an odd function. When $x > 0$, $f(x)=\log_{2}{x}$.

(1) Find the expression of the function $f(x)$ when $x < 0$;

(2) If $g(x)=2^{x}$ $(x\in R)$, set $A={x|f(x)\geqslant 2}$, $B={y|y=g(x), x\in A}$, find the set $B$.

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