
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 equations:<br/>$(1)x^{2}-6x-1=0$ (using the method of completing the square)<br/>$(2)2x^{2}-5x+1=0$ (using the quadratic formula)<br/>$(3)\left(x-2\right)^{2}+x\left(x-2\right)=0$ (using the method of factoring)<br/>$(4)\left(x-3\right)\left(x-1\right)=5$ (choose an appropriate method)

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