
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 the set \( B=\left\{x \in \mathbf{R} \mid x^{2}+(2 a-3) x+2 a^{2}-a-3=0\right\} \), find the range of the real number \( a \) such that \( A \cup B \neq \varnothing \).

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