
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
Define  $f(x) = |x-1|$ . Determine the number of real numbers  $x$  such that  $f(f(\cdots f(f(x))\cdots )) = 0$ , where there are  $2018$   $f$ 's in the equation.

[i]Proposed by Yannick Yao

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