
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 function $f(x)=ax^{2}+(2-a^{2})x-a\ln x$ ($a\in\mathbb{R}$):
1. When $a=-1$, find the extremum of the function $f(x)$;
2. Discuss the monotonicity of the function $f(x)$;
3. When the function $f(x)$ has exactly one zero, analyze the possible values of $a$.

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