
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 $A=\{x\in \mathbb{R} | ax^2-3x+2=0, a\in \mathbb{R}\}$.
1) If $A$ is an empty set, find the range of values for $a$;
2) If $A$ contains only one element, find the value of $a$ and write down this element;
3) If $A$ contains at most one element, find the range of values for $a$.

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