
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
(12 points in total) 4 students are sitting in a row to watch a movie, and there are 6 seats in the row.  
(1) How many seating arrangements are there such that there is exactly one person between students A and B, and there are no empty seats between them?  
(2) How many seating arrangements are there such that all empty seats are not adjacent?

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