
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
Find all real solutions for the equation \(\frac{36}{\sqrt{x}}+\frac{9}{\sqrt{y}}=42-9\sqrt{x}-\sqrt{y}\). Here, if \(x\) is a negative real number, then \(\sqrt{x} = \sqrt{|x|} \mathrm{i}\), where \(\mathrm{i}\) is the imaginary unit.

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