
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 bag contains  $8$  green candies and  $4$  red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers  $m$  and  $n$  so that  $\frac{m}{n}$  is the probability that you do not eat a green candy after you eat a red candy. Find  $m+n$ .

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