
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:  
(1) $(x+3)^2 = (1-2x)^2$;  
(2) $(x+1)^2 = 4x$;  
(3) $2x^2 - 5x + 1 = 0$;  
(4) $(2x-1)^2 = x(3x+2) - 7$.

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