
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
Select $4$ out of $6$ athletes to participate in a $4\times 100$ meter relay race. Under the following conditions, how many different ways are there to arrange them? (Show the calculation process and provide numerical answers)<br/>$(1)$ Athletes A and B must run the middle two legs;<br/>$(2)$ If athletes A and B are both selected, they must run the adjacent two legs.

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