
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 a point $P$ on the graph of the function $f\left( x \right)=\frac{1}{2}\left( {{x}^{3}}-\frac{1}{x} \right)$, and the slope of the tangent line at point $P$ is denoted as $\tan \alpha$, find the range of values for $\alpha$.

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