
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
At the mountain hut, the coach said, "If we continue at this comfortable pace of $4 \mathrm{~km}$ per hour, we will arrive at the station 45 minutes after the departure of our train."

Then he pointed to a group that had just passed us: "They are using poles, and therefore achieve an average speed of $6 \mathrm{~km}$ per hour. They will arrive at the station half an hour before the departure of our train."

How far was the station from the mountain hut?

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