
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 has to travel from City $X$ to City $Y$, then from City $Y$ to City $Z$, and finally from City $Z$ to City $X$. The cities form a right-angled triangle as shown, with $Z$ a distance of $4000\text{ km}$ from $X$ and with $Y$ a distance of $4500\text{ km}$ from $X$. The transportation costs are $\$0.20$ per kilometer for taking a train, and for flying it includes a $\$150$ booking fee plus $\$0.12$ per kilometer. Piravena decides to take the train from $X$ to $Y$. Calculate the cost of the train trip from $X$ to $Y$.

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