
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
 Given that real numbers  $a$ ,  $b$ , and  $c$  satisfy  $ab=3$ ,  $ac=4$ , and  $b+c=5$ , the value of  $bc$  can be written as  $\frac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers. Compute  $m+n$ .


*2021 CCA Math Bonanza Team Round #2*

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