
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 write \( \sqrt{8} + \frac{1}{\sqrt{8}} + \sqrt{9} + \frac{1}{\sqrt{9}} \) in the form \(\dfrac{a\sqrt{8} + b\sqrt{9}}{c}\) such that \(a\), \(b\), and \(c\) are positive integers and \(c\) is as small as possible, then what is \(a+b+c\)?

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