
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
Teressa needs to travel from city $X$ to city $Y$, then from $Y$ to city $Z$, and then from $Z$ to $X$. Each leg of her journey can be done entirely by bus or entirely by airplane. The cities form a right-angled triangle, with $Z$ being a distance of $4000\text{ km}$ from $X$ and $Y$ is $4800\text{ km}$ from $X$. The bus fare costs Teressa $\$0.15$ per kilometer. For flying, she pays a $\$150$ booking fee plus $\$0.12$ per kilometer. If Teressa decides to fly from $X$ to $Y$, determine the cost of her flight.

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