
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
Consider the cubic equation $x^3 + ax + b = 0$, where $a$ and $b$ are real numbers. Identify the conditions from the list below that result in the equation having only one real root. List all correct condition numbers: ① $a=b=-3$; ② $a=-3, b=2$; ③ $a=-3, b>2$; ④ $a=0, b=2$.

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