
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 quadratic equations using appropriate methods:  
(1) $(x-2)^{2}=9$;  
(2) $x(x-3)+x=3$;  
(3) $3x^{2}-1=4x$;  
(4) $(3x-1)^{2}=(x-1)^{2}$.

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