
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 jar contains 97 marbles that are either red, green, or blue. Neil draws two marbles from the jar without replacement and notes that the probability that they would be the same color is \( \frac{5}{12} \). After Neil puts his marbles back, Jerry draws two marbles from the jar with replacement. Compute the probability that the marbles that Jerry draws are the same color.

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