
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
There are 10 sprinters in an international 100-meter race finals. Four of these sprinters are Americans. The medals awarded are gold, silver, and bronze for first, second, and third places respectively. Calculate the number of ways the medals can be awarded given that at most one American can win a medal and exactly one medal must go to a non-American.

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