
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 $y=f\left(x\right)$ is an odd function defined on $\left[-3,3\right]$, when $x\in \left[-3,0\right]$, $f\left(x\right)=\frac{1}{{9}^{x}}+\frac{a}{{4}^{x}}(a∈R)$.<br/>$(Ⅰ)$ Find the analytical expression of $y=f\left(x\right)$ on $\left(0,3\right]$;<br/>$(Ⅱ)$ When $x∈[-1,-\frac{1}{2}]$, the inequality $f(x)≤\frac{m}{{3}^{x}}-\frac{1}{{4}^{x-1}}$ always holds. Find the range of real number $m$.

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