
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 decided to award 12 students who ran the distance in the best time. Each of them needs to be awarded with a "gold," "silver," or "bronze" medal. All three types of medals must be used (at least one of each), and a student who finished earlier cannot be awarded a less valuable medal than the one who finished later.

How many ways can the coach distribute the medals (assuming all runners have different times)?

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