
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 that the function $f(x)$ is an odd function defined on the interval $(-\infty, -1] \cup [1, +\infty)$, and for $x \geqslant 1$, $f(x) = 4x - x^{2}$.  
$(1)$ Find the analytical expression of $f(x)$ when $x \leqslant -1$.  
$(2)$ Find the range of the function $g(x) = \frac{f(x) - 9}{x}$.

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