
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
Ship $A$ is anchored 9 miles from the nearest point $O$ on a straight shoreline. Ship $B$ is anchored 3 miles from the shoreline opposite a point on the shoreline that is 6 miles from $O$. A boat departs from ship $A$ to some point on the shore, picks up a passenger there, and then delivers the passenger to ship $B$. Each mile traveled costs the boat owner 1 dollar regardless of whether the boat carries a passenger or is empty. The passenger pays the boat owner 2 dollars per mile. Where should the boat owner arrange to meet the passenger on the shore in order to maximize their net income (for the route from $A$ to the shore and then to $B$)?

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