
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 dart board looks like three concentric circles with radii of 4, 6, and 8.  Three darts are thrown at the board so that they stick at three random locations on then board.  The probability that one dart sticks in each of the three regions of the dart board is  $\dfrac{m}{n}$  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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