
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
In a different scenario, Agnes needs to travel from $X$ to $Y$, then from $Y$ to $Z$, and finally from $Z$ to $X$. The cities form a right-angled triangle, with $X$ at the right angle. The distance from $X$ to $Z$ is \(4000 \text{ km}\) and from $X$ to $Y$ is \(4500 \text{ km}\). To take a bus, it costs Agnes $\$0.20$ per kilometer. To take an airplane, it costs a $\$120$ booking fee, plus $\$0.12$ per kilometer. Agnes decides to take an airplane from $X$ to $Y$. Calculate the cost of her flight from $X$ to $Y$.

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