
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
You know that the Jones family has five children, and the Smith family has three children.  Of the eight children you know that there are five girls and three boys.  Let  $\dfrac{m}{n}$   be the probability that at least one of the families has only girls for children.  Given that  $m$  and  $n$  are relatively prime positive integers,  find  $m+ n$ .

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