
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
For what values of \(a\) and \(b\) does the equation
\[ x^{2}+2(1+a) x+\left(3 a^{2}+4 a b+4 b^{2}+2\right)=0 \]
have real roots?

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