
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 trip from city $X$ to city $Y$, then from $Y$ to city $Z$, and finally from $Z$ back to $X$. The cities are arranged in a right-angled triangle, with $XZ = 4000$ km and $XY = 5000$ km. Travel costs are as follows: by bus, the cost is $\$0.20$ per kilometer; by airplane, there is a $\$150$ booking fee plus $\$0.15$ per kilometer. Determine the least expensive travel configurations and calculate the total minimum cost for the trip.

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