
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
Select 5 people from 12 to participate in an activity.

(1) How many different ways are there to select if A, B, and C must be chosen?

(2) How many different ways are there to select if only one among A, B, and C is chosen?

(3) How many different ways are there to select if at most two among A, B, and C are chosen?

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