
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
How many different ways can six people line up according to the following different requirements?

1. Six people form a circle;
2. All stand in a row, with A and B must be adjacent;
3. All stand in a row, with A and B not adjacent;
4. All stand in a row, with A, B, and C in order from left to right;
5. All stand in a row, with A and B at the ends;
6. All stand in a row, with A not at the left end and B not at the right end.

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