
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 using the specified methods:<br/>
(1) $x^{2}-4x-2=0$ (using factoring method);<br/>
(2) $2y^{2}-3y-1=0$ (using formula method);<br/>
(3) $3x(x-1)=2-2x$ (using appropriate method);<br/>
(4) $2x^{2}-x-1=0$ (using factoring method).

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