
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]


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Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$, and for any $n\in\mathbb{N}^*$, the point $(a_n,S_n)$ lies on the graph of the function $f(x)=-\frac{1}{2}x+\frac{1}{2}$.  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$.  
(Ⅱ) Let $b_n= \frac{3}{2}\log_{3}(1-2S_n)+10$, find the maximum value of 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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