
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 \\({{x}^{3}}-ax+b=0\\), where \\(a,b\\) are real numbers. Among the following conditions, those that result in the cubic equation having only one real root are (write down all the correct condition numbers):

\\(①a=0\\), \\(b=2;②a=-3\\), \\(b=2;③a=3\\), \\(b=2;④a=3\\), \\(b=1;⑤a=3\\), \\(b=-3\\)

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