
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
A box contains $500$ red marbles, $700$ black marbles, and $800$ blue marbles. Determine $|P_s - P_d|$, where $P_s$ is the probability that two randomly drawn marbles are of the same color, and $P_d$ is the probability that they are of different colors.
A) $\frac{31}{100}$
B) $\frac{1}{64}$
C) $\frac{21}{200}$
D) $\frac{13}{50}$

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