
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 travel from city $A$ to city $B$, then from $B$ to city $C$, and finally from $C$ back to $A$. Each leg of the trip is either by bus or by airplane. The cities form a right-angled triangle with $C$ being 3500 km from $A$ and $B$ being 4000 km from $A$. For bus travel, it costs Piravena $\$0.15$ per kilometer, and for airplane travel, it costs a $\$100$ booking fee plus $\$0.10$ per kilometer. Determine the total distance Piravena travels on her entire trip.

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