
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
How long would it take for the Earth to complete its axial rotation so that the resulting centrifugal force at the equator nullifies the weight of objects? Additionally, through trial and error, solve the question of at what distance from the Earth, given the current rotational speed, the centrifugal force would equal the gravitational force?

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