
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 travel from city $A$ to city $B$, from $B$ to city $C$, and from $C$ back to $A$ completing a triangle. The triangle formed by the cities is right-angled at $C$, with $CA = 4000$ km and $AB = 4500$ km. Transportation choices are either bus or airplane, where the bus costs $\$0.20$ per kilometer, and the airplane costs $\$120$ booking fee plus $\$0.12$ per kilometer. As usual, Piravena will choose the cheapest option for each leg of the journey. What is the total cost of her trip?

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