
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
Simplify first and then evaluate the following expression:

\[
\left(\frac{x(x+y)+2y(x+y)}{xy(x+2y)}\right) \div \left(\frac{xy}{x+2y}\right)
\]

where \(x = 3\sqrt{3} + 2\sqrt{2}\) and \(y = 3\sqrt{3} - 2\sqrt{2}\).

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