
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
Find the relationship between the falling speed of a body in the air and time, if the air resistance force is proportional to the square of the speed $v$ and the area $S$ of the largest section of the body perpendicular to the direction of motion, $F=k S v^{2}$.

Then find: 1) the behavior of the falling speed of the body as time increases and 2) the radius of a parachute so that the maximum falling speed does not exceed 5 m/s, given that the combined weight of the parachute and parachutist is 100 kg, assuming $k=0.083$.

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