
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
(This question is worth a total of 13 points)  
(1) If 3 people are to sit in a row of eight seats, with the requirement that there must be an empty seat on both sides of each person, how many different seating arrangements are possible?  
(2) If 5 people stand in a row, and person A must be to the right of person B, how many different arrangements are possible?  
(3) There are 10 guaranteed university admission spots to be distributed among 7 schools, with each school receiving at least one spot. How many different ways can the spots be distributed?

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