
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 gravitational force that Earth exerts on a satellite is inversely proportional to the square of the distance between the center of the Earth and the satellite. When a satellite is at a usual operation altitude 1,000 miles from the center of the Earth, the gravitational force is 500 Newtons. What is the gravitational force (in Newtons) that Earth exerts on this satellite if it moves to an orbital distance of 10,000 miles from the Earth’s center? Express your answer as a fraction.

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