
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
There are  $ 6n \plus{} 4$  mathematicians participating in a conference which includes  $ 2n \plus{} 1$  meetings. Each meeting has one round table that suits for  $ 4$  people and  $ n$  round tables that each table suits for  $ 6$  people. We have known that two arbitrary people sit next to or have opposite places doesn't exceed one time. 
1. Determine whether or not there is the case  $ n \equal{} 1$ .
2. Determine whether or not there is the case  $ n > 1$ .

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