
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 sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}=n-2a_{n}+20$.  
$(Ⅰ)$ Find the general formula for $\{a_{n}\}$.  
$(Ⅱ)$ Let $b_{n}={\log}_{\frac{2}{3}}\frac{{a}_{1}-1}{9}+{\log}_{\frac{2}{3}}\frac{{a}_{2}-1}{9}+\ldots +{\log}_{\frac{2}{3}}\frac{{a}_{n}-1}{9}$. Find the sum $T_{n}$ of the first $n$ terms of $\{\frac{1}{{b}_{n}}\}$.

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