
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
The extracurricular activity group consists of 13 people, including 8 boys and 5 girls. Each gender has a designated leader. Now, 5 people are to be selected to host a certain activity. How many ways can the selection be made under the following conditions?

(1) Only 1 girl is selected;

(2) Both leaders are selected;

(3) At least 1 leader is selected.

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