
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 $\sqrt{3}+\frac{1}{\sqrt{3}} + \sqrt{7} + \frac{1}{\sqrt{7}}$ in the form $\dfrac{a\sqrt{3} + b\sqrt{7}}{c}$ such that $a$, $b$, and $c$ are positive integers with $c$ as minimal as possible, what is $a+b+c$?

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