
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 person wants to take a bus but doesn't want to wait at the station. He rides a motorcycle from one bus stop to another, traveling at a speed of $\frac{1}{3}$ of the bus's speed. When he sees the bus approaching in his rearview mirror, he is 2 km away from the bus. At this moment, he has two options:
(1) Immediately turn around and ride towards the bus to catch it at the previous bus stop;
(2) Continue riding to the next bus stop to catch the bus there.
What is the maximum distance between bus stops to ensure that this person will not miss the bus?

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