
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 $f(x)=\begin{cases} & -{{2}^{{ }\\!\\!|\\!\\!{ x-1 }\\!\\!|\\!\\!{ }}}+3,0 \leqslant x < 2 \\\\ & \frac{1}{2}f(x-2),x \geqslant 2 \\\\ \end{cases}$, find the number of zeros of the function $g(x)=xf(x)-1$.

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