
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
Given that $a$ and $b$ are integers, and $a>b$, the two roots of the equation $3x^2 + 3(a+b)x + 4ab = 0$ satisfy the relationship $\alpha(\alpha+1) + \beta(\beta+1) = (\alpha+1)(\beta+1)$. Determine all pairs of integer points $(a,b)$.

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