
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
Determine the pairs of values of \(x\) and \(y\) that are the common solutions of the equations \(y = (2x+1)^2\) and \(2xy + y = 3\).
A) 3 real pairs  
B) 4 real pairs  
C) 4 imaginary pairs  
D) 1 real and 2 imaginary pairs  
E) 0 real and 3 imaginary pairs

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