
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 a satellite exerts on an object is inversely proportional to the square of the distance between the center of the satellite and the object. If the gravitational force is 200 Newtons when an astronaut is 100 miles from the center of the satellite, find the gravitational force when the astronaut is 500 miles from the center. Assume that the satellite's mass increases, doubling the initial gravitational constant used. Express your answer as a fraction.

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