
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
Carlos must make a journey from $X$ to $Y$, then from $Y$ to $Z$, then from $Z$ to $X$. The cities form a right-angled triangle, with $XZ$ being the hypotenuse of length 4000 km, and $XY$ being one of the legs with a length of 3500 km. Travel options include either a train which costs $\$0.20$ per kilometer or a taxi which includes a $\$150$ booking fee plus $\$0.15$ per kilometer.

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