
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 function $f(x)= 
\begin{cases} 
3-2x, & x\leq 1\\
x^2, & x > 1
\end{cases}$, find the number of zeros of the function $g(x)=f(x)-2$.

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