
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
 $f$  is a function on the set of complex numbers such that  $f(z)=1/(z*)$ , where  $z*$  is the complex conjugate of  $z$ .  $S$  is the set of complex numbers  $z$  such that the real part of  $f(z)$  lies between  $1/2020$  and  $1/2018$ . If  $S$  is treated as a subset of the complex plane, the area of  $S$  can be expressed as  $m× \pi$  where  $m$  is an integer. What is the value of  $m$ ? 

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