
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
For every integer $k$ with $k > 0$, let $R(k)$ be the probability that
\[
\left[\frac{n}{k}\right] + \left[\frac{200 - n}{k}\right] = \left[\frac{200}{k}\right]
\]
for an integer $n$ randomly chosen from the interval $1 \leq n \leq 199$. What is the minimum possible value of $R(k)$ over the integers $k$ in the interval $1 \leq k \leq 199$?
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) $\frac{2}{3}$
D) $\frac{3}{4}$
E) $\frac{4}{5}$

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