
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
Customs anti-smuggling speedboats, when fully fueled, can travel 150 nautical miles. There are 3 such speedboats starting from the customs office simultaneously for a patrol mission and they all need to return after the mission. To maximize the patrol range, at a certain point during the patrol, two of the boats will keep just enough fuel for their return and transfer the remaining fuel to the third boat. What is the maximum distance from the customs office that the third boat can patrol?

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