
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 the solution set of the inequality $x^{2}-2x+1-m^{2} \lt 0$ is $A$;  
$(1)$ Find $A$;  
$(2)$ If $0 \lt m \lt 1$, and $A=\{x\left|\right.a \lt x \lt b\}$, find the minimum value of $\frac{1}{{8a+2b}}-\frac{1}{{3a-3b}}$.

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