
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 $f(x)$ is an odd function defined on $\mathbb{R}$, and when $x \geqslant 0$, $f(x) = m - 3^{x}$  
$(1)$ Find the expression for the function $f(x)$;  
$(2)$ When $x \in [2, 8]$, the inequality $f((\log_{2}x)^{2}) + f(5-a\log_{2}x) \geqslant 0$ always holds, find the range of the real number $a$.

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