
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
Solve the following equations using appropriate methods:  
(1) $x^2-2x+1=0$  
(2) $x^2+2x-3=0$ (use the completing square method)  
(3) $2x^2+5x-1=0$ (use the quadratic formula)  
(4) $2(x-3)^2=x^2-9$.

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