
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
Consider that Piravena must make a round trip from $A$ to $B$ and back from $B$ to $A$. The cities still form a right-angled triangle, with $C$ a distance of $3000\text{ km}$ from $A$. The distance from $A$ to $B$ is now increased to $4000\text{ km}$. To take a bus, it now costs Piravena $\$0.20$ per kilometer. To take an airplane, it costs her a $\$120$ booking fee, plus $\$0.12$ per kilometer. She decides to fly from $A$ to $B$ but returns by bus. Calculate the total cost of Piravena’s round trip.

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