
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 for $x$ using the prescribed methods:
1. $(x-1)^2-4=0$
2. $(2x-1)(x+3)=4$
3. $2x^2-5x+2=0$ (by completing the square)

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