
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 sets $A=\{x|x^{2}+2x-3=0\}$ and $B=\{x|x=-\frac{1}{2a}\}$, choose one of the following conditions: ①$A\cap B=B$, ②$(\complement _{R}B)\cap A=\{1\}$, ③$A\cap B=\varnothing$. Then solve the problem: Find the set of real numbers $a$ that satisfy the chosen condition.

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