
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 for any $x \in (-\infty, 0) \cup (0, +\infty)$ and $y \in [-1, 1]$, the inequality $x^{2}+ \frac{16}{x^{2}}-2xy- \frac{8}{x} \sqrt{1-y^{2}}-a \geqslant 0$ always holds, the range of the real number $a$ is $\_\_\_\_\_\_\_.$

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