
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
Piravena needs to make a trip from city $D$ to $E$, then from $E$ to $F$, then from $F$ to $D$. The cities form a right-angled triangle with $F$ as the right angle. The distances are as follows: from $D$ to $F$ is 2000 km, and from $D$ to $E$ is 4500 km. The cost per kilometer for a bus is $\$0.18$, and for an airplane, there's a $\$120$ booking fee plus $\$0.12$ per kilometer. Determine the total distance Piravena travels.

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