
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 density of a solid sphere depends solely on the radial distance. The gravitational force at any point inside the sphere, a distance \( r \) from the center, is \( kr^2 \) (where \( k \) is a constant). Find the density (in terms of \( G, k \) and \( r \)), and the gravitational force at a point outside the sphere. [You may assume the usual results about the gravitational attraction of a spherical shell.]

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