
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 new scenario, city $D$, $E$, and $F$ form a right-angled triangle with $D$ being the right-angle. The distance from $D$ to $E$ is $4000\text{ km}$, from $E$ to $F$ is $4500\text{ km}$, and from $F$ to $D$ is $5000\text{ km}$. For buses, the fare is $\$0.20$ per kilometer. Airplanes charge a $\$120$ booking fee when flying from $D$ or $F$ but a $\$150$ booking fee from $E$, plus $\$0.12$ per kilometer regardless of the departure. Piravena decides to take a bus from $D$ to $E$ and fly from $E$ to $F$. Calculate the total travel cost for Piravena from $D$ to $F$ via $E$.

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