
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 the sequence $\{a_n\}$ with the sum of its first $n$ terms $S_n = n^2 + 2n$, and a positive geometric sequence $\{b_n\}$ satisfies: $b_1 = a_1 - 1$, and $b_4 = 2b_2 + b_3$.  
(Ⅰ) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) If the sequence $\{c_n\}$ satisfies: $c_n = \frac{a_n}{b_n}$, with the sum of its first $n$ terms as $T_n$, find the range of $T_n$.

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