
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
Maria must make a trip from $X$ to $Y$, then from $Y$ to $Z$, then from $Z$ to $X$. Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle with $Z$ a distance of 4000 km from $X$ and with $Y$ a distance of 4500 km from $X$. The cost to take a bus is $\$0.20$ per kilometer. To take an airplane, it costs her a $\$120$ booking fee, plus $\$0.12$ per kilometer.

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