
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
Jar #1 contains five red marbles, three blue marbles, and one green marble.
Jar #2 contains five blue marbles, three green marbles, and one red marble.
Jar #3 contains five green marbles, three red marbles, and one blue marble.
You randomly select one marble from each jar. Given that you select one marble of each color, the probability that the red marble came from jar #1, the blue marble came from jar #2, and the green marble came from jar #3 can be expressed as  $\frac{m}{n}$ , where m and n are relatively prime positive integers. Find m + n.

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