
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
Combine $2n$ new soldiers into $n$ groups of 2 people for machine gun shooting practice:
1. One person learns to be the main shooter, and the other the assistant shooter.
2. The two people are not divided into main and assistant.

How many ways are there to form the groups for each case?

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