
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
Find all pairs \((a,b)\) of non-zero real numbers that satisfy the equation
\[\frac{a^2}{b} + \frac{b^2}{a} = \frac{(a+b)^2}{a+b}\]
A) none  
B) 1  
C) 2  
D) one pair for each \( b \neq 0 \)  
E) two pairs for each \( b \neq 0 \)

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