
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 needs to make a trip from $A$ to $B$, then from $B$ to $C$, then from $C$ to $A$. The cities form a right-angled triangle, with the angles at $B$. $AB$ is 4000 km and $AC$ is 4800 km. To take a bus, it costs Piravena $\$0.18$ per kilometer. To take an airplane, it costs her a $\$120$ booking fee, plus $\$0.12$ per kilometer. Determine the total distance traveled by Piravena and the most cost-effective way for this travel.

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