
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
Let's solve a similar problem where Eleonora must travel from city $X$ to $Y$, then from $Y$ to $Z$, then from $Z$ to $X$. The cities form a right-angled triangle with $Z$ a distance of 4000 km from $X$ and with $Y$ a distance of 4500 km from $X$. Traveling by bus costs Eleonora $\$0.20$ per kilometer. Traveling by airplane costs a $\$150$ booking fee, plus $\$0.15$ per kilometer. She selects the least expensive way to travel between cities. Calculate the total cost for Eleonora's trip.

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