
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
If we express $\sqrt{6} + \frac{1}{\sqrt{6}} + \sqrt{8} + \frac{1}{\sqrt{8}}$ in the form $\dfrac{p\sqrt{6} + q\sqrt{8}}{r}$ where $p$, $q$, and $r$ are positive integers and $r$ is minimized, what is $p+q+r$?

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