
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 plans a trip involving three cities $A$, $B$, and $C$ which form a right-angled triangle. City $C$ is directly south of $B$ and directly west of $A$. The distance from $A$ to $B$ is $4000$ km and from $B$ to $C$ is $3000$ km. Her trip starts from $A$ to $B$ by airplane, then from $B$ to $C$ by bus. The cost of taking a bus is $\$0.20$ per kilometer, while flying involves a $\$150$ booking fee plus $\$0.12$ per kilometer. Determine the total cost for Piravena to travel from $A$ to $B$ by air.

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