
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 signum function \\(sgn(x)= \begin{cases} 1,x > 0 \\ 0,x=0 \\ -1,x < 0\\end{cases}\\) and \\(f(x)=x^{2}-2x\\), find the number of zeros of the function \\(F(x)=sgn[f(x)]-f(x)\\).

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