
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
Piravena must make a trip from \(A\) to \(B\), then from \(B\) to \(C\), then from \(C\) to \(A\). Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with \(C\) a distance of 3500 km from \(A\) and with \(B\) a distance of 3700 km from \(A\). To take a bus, it costs Piravena \$0.20 per kilometer. To take an airplane, it costs her a \$120 booking fee, plus \$0.12 per kilometer. Determine the distance she travels for her complete trip, assuming she uses only the airplane for the longest leg of the trip.

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