
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
Several people participated in a race, including Andrei, Dima, and Lenya. No two participants finished simultaneously.

- The number of people who finished before Andrei is half the number of people who finished after him.
- The number of people who finished before Dima is a third of the number of people who finished after him.
- The number of people who finished before Lenya is a quarter of the number of people who finished after him.

What is the minimum number of people that could have participated in the race?

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