
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 small town, three main straight highways converge pairwise at points A, B, and C. There is also a ring road passing through points A, B, and C, forming a circle. The lengths of the highways inside the circle are 7, 8, and 9 kilometers. In the center of this circle, there is a local landmark - a television tower. Within the town is a beautiful botanical garden, whose area is bounded by a cypress hedge planted along another circle such that the hedge touches each of the highways exactly once. The town authorities plan to build a hanging pedestrian bridge from the center of the botanical garden directly to the television tower. Calculate the estimated cost of building this bridge if it is 1000 currency units per kilometer of distance between the center of the botanical garden and the television tower.

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