
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
Seven people stand in a row. (Write out the necessary process, and use numbers for the answers)  
(1) How many ways can person A and person B stand next to each other?  
(2) How many ways can person A and person B stand not next to each other?  
(3) How many ways can person A, person B, and person C stand so that no two of them are next to each other?  
(4) How many ways can person A, person B, and person C stand so that at most two of them are not next to each other?

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