
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
From a group of $4$ boys and $3$ girls, select three representatives.

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

$(2)$ How many different ways are there to make the selection if at least one girl must be chosen?

$(3)$ How many different ways are there to make the selection if both boys and girls must be chosen? (Show necessary processes)

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