
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 sets 
\[A = \left\{ t \mid t, \text{ such that } \left\{ x \mid x^2 + 2tx - 4t - 3 \neq 0 \right\} = \mathbf{R} \right\}\]
\[B = \left\{ t \mid t, \text{ such that } \left\{ x \mid x^2 + 2tx - 2t = 0 \right\} \neq \varnothing \right\}\]
where \(x\) and \(t\) are real numbers, find \(A \cap B\).

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