
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
There are $1500$ red marbles and $2500$ black marbles in a box. Let $P_s$ be the probability that two marbles drawn at random from the box are the same color, and let $P_d$ be the probability that they are different colors. Find $|P_s - P_d|.$
A) $\frac{1}{100}$
B) $\frac{1}{50}$
C) $\frac{3}{50}$
D) $\frac{6}{100}$
E) $\frac{1}{25}$

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