
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
4.  Consider spherical surface  $S$  which radius is  $1$ , central point  $(0,0,1)$  in  $xyz$  space.  If point  $Q$  move to points on S expect  $(0,0,2)$ .  Let  $R$  be an intersection of plane  $z=0$  and line  $l$  pass point  $Q$  and point  $P (1,0,2)$ .  Find the range of moving  $R$ , then illustrate it.

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