
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
Let the universal set be $\mathbb{R}$, and let $A=\left\{x\in\mathbb{R}\setminus\mathbb{Q}\ \middle|\ \sqrt{3}x^2-(2\sqrt{3}-\sqrt{2})x-2\sqrt{2}=0\right\}$. Find the element(s) of $A$.

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