
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
A coach has a team of $30$ players. He needs to split the players into equal groups of at most $12$ players each. Additionally, one of the groups needs to be exactly half the size of another group. What is the least number of groups the coach needs?

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