
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 $2\sqrt{3}+\frac{2}{\sqrt{3}} + 3\sqrt{2} + \frac{3}{\sqrt{2}}$ in the form $\dfrac{a\sqrt{3} + b\sqrt{2}}{c}$ 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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