
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 journey consisting of three legs forming a right-angled triangle, city $C$ is $4000$ km from city $A$, and city $B$ is located such that the distance from $B$ to $A$ is $4500$ km. Piravena can either take a bus, which costs $\$0.20$ per kilometer, or an airplane, which includes a $\$120$ booking fee plus $\$0.12$ per kilometer. She starts her trip by flying from $C$ to $B$. Calculate the cost for Piravena to fly from $C$ to $B$.

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