
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
From a set of 32 chess pieces, two pieces are drawn randomly. What is the probability that:

a) 2 dark pieces or 2 pieces of different colors,

b) 1 bishop and 1 pawn or 2 pieces of different colors,

c) 2 different-colored rooks or 2 pieces of the same color but different sizes,

d) 1 king and one knight of the same color, or two pieces of the same color,

e) 2 pieces of the same size or 2 pieces of the same color

are drawn?

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