
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
From 8 athletes, select 4 to participate in a 4×100-meter relay race. Under the following conditions, how many different arrangements are there? (End with numbers)
(1) Athletes A and B must run the middle two legs;
(2) If only one of A and B is selected and cannot run the middle two legs;
(3) If both A and B are selected and must run adjacent legs.

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