
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 round trip starting from city $X$, going to $Y$, then to $Z$, and back to $X$. The cities form a right-angled triangle with $X$ at the right angle. The distance from $X$ to $Y$ is $4000\text{ km}$, and from $Y$ to $Z$ is $3000\text{ km}$. For transportation, Piravena can either take a bus, costing $\$0.20$ per kilometer, or an airplane, costing a $\$120$ booking fee plus $\$0.12$ per kilometer. She decides to fly from $X$ to $Y$ and take a bus from $Y$ to $Z$ and from $Z$ to $X$. Determine the total cost for Piravena's round trip.

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