
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 $A=\{x|2x^2+x-3=0\}$, the set $B=\{i|i^2\geq4\}$, and the complement of set $C$ in the real numbers, $\complement_{\mathbb{R}}C=\{-1, 1, \frac{3}{2}\}$, find the intersection of set B and the union of set A and the complement of set C.

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