
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 triangular trip from $A$ to $B$, from $B$ to $C$, and from $C$ back to $A$. Each leg of the trip is made entirely by car or train. The cities form a right-angled triangle as shown, with $C$ a distance of 4000 km from $A$ and $B$ a distance of 5000 km from $A$. The cost of traveling by car is $\$0.20$ per kilometer. The cost of taking a train is a $\$150$ booking fee, plus $\$0.15$ per kilometer.

Calculate the least expensive way for Piravena to complete her trip and find the total cost.

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