
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 again make a trip from $A$ to $B$, then from $B$ to $C$, and finally from $C$ back to $A$. The cities now form a right-angled triangle, where $C$ is 3500 km from $A$ and $B$ is a distance of 4000 km from $A$. The cost to take a bus is $\$0.18$ per kilometer. To take an airplane, it costs a $\$120$ booking fee, plus $\$0.12$ per kilometer.

Piravena chooses the least expensive route, assuming the booking fee for flights is discounted by 50% when making more than one flight. Calculate the total cost of Piravena's trip.

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