
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
Dima and Serezha decided to hold a race on a circular lake. They start simultaneously from the same point. Serezha rides a motorboat at a constant speed of 20 km/h and somehow crosses the lake (not necessarily via the diameter) in 30 minutes. Meanwhile, Dima runs along the shore of the lake for the first 15 minutes at a speed of 6 km/h, and then for the remaining time, he moves at a constant speed by boat to the other shore, parallel to Serezha's trajectory. After simultaneously arriving at the opposite shore, the boys run towards each other. During the entire race, the boys run at constant and equal speeds. How much time after they part will they meet?

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