
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 8 boys and 5 girls. Choose 6 people from them.

(1) How many different ways are there to make the selection?

(2) How many different ways are there if there are exactly 3 girls?

(3) How many different ways are there if there are at most 3 girls?

(4) How many different ways are there if there are both boys and girls?

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