
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 the expression of the function $y=f\left(x\right)$ as $f\left(x\right)=2^{x}-2^{-x}$.  
$(1)$ Find the zeros of the function $y=f\left(x\right)$;  
$(2)$ Solve the inequality: $f\left(x\right) \lt 2$;  
$(3)$ If the equation about $x$ $f\left(x\right)=m\cdot 2^{x}-2^{1-x}-\frac{4}{3}m$ has only one real root, find the range of real number $m$.

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