
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
Janet must travel from City $D$ to City $E$, then from City $E$ to City $F$, and from City $F$ back to City $D$. Each leg of the journey is either by bus or airplane. These cities form a right-angled triangle, with $F$ being $4000\text{ km}$ from $D$ and with $E$ a distance of $4750\text{ km}$ from $D$. Taking a bus costs $\$0.20$ per kilometer. Taking an airplane costs a $\$150$ booking fee plus $\$0.12$ per kilometer. Janet starts her trip by flying from $D$ to $E$. Calculate the cost for Janet to fly from $D$ to $E$.

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