
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}
user