
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
Three runners move along a circular track at equal constant speeds. When two runners meet, they instantly turn around and start running in the opposite direction.

At a certain moment, the first runner met the second runner. After 20 minutes, the second runner met the third runner for the first time. Another half hour later, the third runner met the first runner for the first time.

How many minutes does it take for one runner to complete the entire track?

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