
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 functions $f(x)=x\ln x$ and $g(x)=-x^{2}-ax-4$ where $a\in \mathbb{R}$. Find:
1. The extreme values of the function $f(x)$.
2. If the inequality $f(x) > \frac{1}{3}g(x)$ holds for all $x\in (0,+\infty)$, find the range of values for $a$.

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