
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 equation by an appropriate method:  
(1) $x^2-5x=0$  
(2) $(2x+1)^2=4$  
(3) $x(x-1)+3(x-1)=0$  
(4) $x^2-2x-8=0$．

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