
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
The main street of the village (also called Main Street) is perpendicular to General de Gaulle Street, intersecting at the Town Hall Square. The Catholic cathedral faces Main Street, while the Protestant cathedral faces General de Gaulle Street. The school is on a street that connects these two cathedrals, at a bird's flight distance (500 m) from each of the mentioned streets. All the streets are straight. One day, the teacher asked the students to calculate the sum of the reciprocals of the distances (in meters) from the town hall to each of the cathedrals. The students did not know either trigonometry or analytical geometry.

What did they answer their teacher?

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