
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 must make a trip from $A$ to $B$, then from $B$ to $C$, and finally from $C$ back to $A$. The cities form a right-angled triangle, with $C$ at $3000\text{ km}$ from $A$, $B$ at $4000\text{ km}$ from $A$, and the right angle at $C$. She starts her trip by taking a bus from $A$ to $C$. Afterwards, she needs to go from $C$ to $B$ using a combination of a flight and a bus. The first half of the distance she will fly and the second half she will take a bus. It costs $\$0.20$ per kilometer to take a bus, and to take an airplane, it costs her a $\$150$ booking fee plus $\$0.12$ per kilometer. Calculate the combined cost of her journey from $C$ to $B$.

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