
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
Below is the process written by Teacher Yang on the blackboard when explaining the solution to a quadratic equation. Please read carefully and complete the tasks.

$2x^{2}-3x-5=0$  
Solution: $x^{2}-\frac{3}{2}x=\frac{5}{2}$ Step 1  
$x^{2}-\frac{3}{2}x+(\frac{3}{4})^{2}=\frac{5}{2}+(\frac{3}{4})^{2}$ Step 2  
$(x-\frac{3}{4})^{2}=\frac{49}{16}$ Step 3  
$x-\frac{3}{4}=\pm \frac{7}{4}$ Step 4  
$x_1=\frac{5}{2},x_2=-1$ Step 5  
(1) Task 1: ①Xiaoying's method of solving the equation is ______.  
$A$. direct square root method; $B$. completing the square method; $C$. formula method; $D$. factoring method.  
②The basis for the transformation in the second step is ______.  
(2) Task 2: Please solve the following equations as required:  
①$x^{2}+2x-3=0$ (formula method)  
②$3\left(x-2\right)^{2}=x^{2}-4$ (factoring method)

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