
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 an odd function $f(x)$ defined on $\left[-4,4\right]$, when $x\in \left[-4,0\right]$, $f(x)=\frac{1}{{4^x}}+\frac{a}{{3^x}}$. <br/>$(1)$ Find the analytical expression of the function $f(x)$; <br/>$(2)$ If there exists $x\in \left[-2,-1\right]$, such that the inequality $f(x)≤\frac{m}{{2^x}}-\frac{1}{{3^{x-1}}}$ holds, find the range of real number $m$.

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