
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 $1500$ red marbles and $2000$ black marbles. Define $P_s$ as the probability that two randomly drawn marbles are the same color, and $P_d$ as the probability that they are different colors. Find $|P_s - P_d|$.
A) $\frac{1}{25}$
B) $\frac{1}{49}$
C) $\frac{1}{50}$
D) $\frac{1}{51}$
E) $\frac{1}{100}$

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