
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
Calista needs to make a trip from City $X$ to City $Y$, then from City $Y$ to City $Z$, and finally from City $Z$ back to City $X$. The cities form a right-angled triangle, with city $Z$ being a distance of 4000 km from $X$, and $Y$ being a distance of 4500 km from $X$. Taking the bus costs Calista $\$0.20$ per kilometer. Taking an airplane costs her a $\$120$ booking fee plus $\$0.12$ per kilometer. Calista chooses the least expensive option to travel between each pair of cities. What is the total cost of her trip?

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