
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 a sequence $\{a_{n}\}$ where all terms are positive numbers and satisfy ${a}_{n+1}({a}_{n+1}-{a}_{n})=2{a}_{n}^{2}$, and $a_{1}a_{2}a_{3}=8$.<br/>$(1)$ Find the general formula for $\{a_{n}\}$;<br/>$(2)$ If ${b}_{n}=\frac{lo{g}_{2}{a}_{n+1}}{{a}_{n}}$, find the sum of the first $n$ terms of the sequence $\{b_{n}\}$ denoted as $T_{n}$.

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