
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
Assuming cities A, B, and C form a right-angled triangle with C as the right angle, clarify Piravena's cost if she decides to fly from B to C. The distance from B to C is $1000 \text{ km}$ and the distance from A to C remains $3000 \text{ km}$, thus making the distance from A to B $2236.07 \text{ km}$ (calculated via Pythagoras' theorem). The cost to fly includes a $\$100$ booking fee, plus $\$0.10$ per kilometer.

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