
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 journey between three cities, $X, Y, Z$, forming a right-angled triangle, $Z$ is 4000 km from $X$, and $Y$ is 4500 km from $X$. The hypotenuse $YZ$ hence needs to be calculated. The cost to take a bus is $\$0.20$ per kilometer, and to take a flight, there is a $\$120$ booking fee plus $\$0.12$ per kilometer. Luna starts her travel by taking a bus from $X$ to $Y$. Calculate the cost for her to bus from $X$ to $Y$.

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