
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

	 For positive integers  $n$ , let  $S_n$  be the set of integers  $x$  such that  $n$  distinct lines, no three concurrent, can divide a plane into  $x$  regions (for example,  $S_2=\{3,4\}$ , because the plane is divided into 3 regions if the two lines are parallel, and 4 regions otherwise). What is the minimum  $i$  such that  $S_i$  contains at least 4 elements?


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