
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 and find the value of: $\sqrt{2x}•\sqrt{\frac{x}{y}}•(\sqrt{\frac{y}{x}}+\sqrt{\frac{1}{y}})$, where real numbers $x$ and $y$ satisfy $y=\sqrt{x-3}+\sqrt{6-2x}+2$.

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