
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
There are 7 male athletes and 3 female athletes. They are to march in a parade. If the first and last athletes must be male, and the female athletes cannot be adjacent, how many different arrangements are possible? Additionally, how many arrangements are there if the female athletes are together and placed at both ends of the line? Lastly, how many arrangements are there if the female athletes are simply together in the lineup?

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