
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
6 people are to be seated in a row of 10 seats. Calculate:  
(1) How many seating arrangements are there such that no two empty seats are adjacent?  
(2) How many seating arrangements are there such that exactly 3 out of the 4 empty seats are adjacent?  
(3) How many seating arrangements are there such that at most 2 out of the 4 empty seats are adjacent?

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