
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
Harry, Ron, Hermione, and Neville are having a race on their broomsticks. Hermione has a magic speed boost that guarantees she won't finish last. If there are no ties, in how many different possible orders can they finish, considering Hermione's boost?

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