
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
Read the material and answer the questions.  
When studying quadratic equations, Xiaoming solved the equation $2x^{2}-8x+5=0$ as follows:  
Solution: $2x^{2}-8x+5=0$.  
$2x^{2}-8x=-5$. (1)  
$x^2-4x=-\frac{5}{2}$. (2)  
$x^2-4x+4=-\frac{5}{2}+4$. (3)  
$(x-2)^2=\frac{3}{2}$. (4)  
$x-2=\frac{\sqrt{6}}{2}$. (5)  
$x=2+\frac{\sqrt{6}}{2}$. (6)  
Question: (1) In the above process, the error occurred starting from step ______ (fill in the number);  
(2) The reason for the error is: ______;  
(3) Write down the solution to this equation: ______.

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