
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
In a box, there are 2003 red marbles and 1999 black marbles. Let $P_s$ be the probability that two marbles drawn at random from the box are of the same color, and let $P_d$ be the probability that they are of different colors. Calculate $|P_s - P_d|$.
A) $\frac{5993}{8004001}$
B) $\frac{5993}{16008001}$
C) $\frac{1}{1333}$
D) $\frac{1}{2667}$

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