
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 sportsman walking along a highway noticed that every 6 minutes, a trolleybus catches up with him, and every 3 minutes, a trolleybus passes him coming from the opposite direction. Find the intervals at which trolleybuses depart from the terminals and determine how many times slower the sportsman walks compared to the trolleybus, assuming that the trolleybuses depart at equal intervals in both directions and travel without stops at a constant and identical speed.

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