
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) = $$\begin{cases} 1, x > 0 \\ 0, x = 0 \\ -1, x < 0 \end{cases}$$, find the set of all zeros of the function f(x) = sgn(x) - 2x.

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