
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
Everyone knows that when using the completing the square method to solve a general form of a quadratic equation, we need to first make the coefficient of the quadratic term equal to $1$ and then proceed with completing the square. Now, please read the solution process below for equation (1) and solve equation (2) using the same method.  
Equation (1): $2x^2-2\sqrt{2}x-3=0$.  
Solution:  
$2x^2-2\sqrt{2}x-3=0$,  
$(\sqrt{2}x)^2-2\sqrt{2}x+1=3+1$,  
$(\sqrt{2}x-1)^2=4$,  
$\sqrt{2}x-1=\pm2$,  
$x_1=-\frac{\sqrt{2}}{2}$, $x_2=\frac{3\sqrt{2}}{2}$.  
Equation (2): $5x^2-2\sqrt{15}x=2$.

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