
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
For any real numbers $a$ and $b$, we define: $a\otimes b=\left\{\begin{array}{l}{\frac{b}{4a-b}, a≥b}\\{\frac{a}{4a+b}, a＜b}\end{array}\right.$.<br/>According to the above definition, solve the following problems:<br/>$(1)$ Calculate: $(-\frac{1}{2})\otimes \left(-1\right)=$____.<br/>$(2)$ If $\left(x-3\right)\otimes \left(x+3\right)=1$, then $x=$____.

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