
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 6 male athletes and 4 female athletes, including one male captain and one female captain. Determine the number of ways to select a team of 5 athletes out of the 10 to participate in an external competition under the following conditions:
(1) The team is to consist of 3 male athletes and 2 female athletes;
(2) The team includes at least one female athlete;
(3) The team includes at least one of the captains (male or female);
(4) The team includes at least one captain and at least one female athlete.

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