
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. Use the factorization method for (1) and (2):
(1) $(3x-1)^2 = (x+1)^2$   
(2) $(x-1)^2+2x(x-1)=0$  
(3) Solve the equation using the completing the square method: $x^2 - 4x + 1 = 0$  
(4) $2x^2 + 7x - 4 = 0$ (use the quadratic formula)

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