
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 an arithmetic sequence $\{a_n\}$, with its sum of first $n$ terms denoted as $S_n$, and a geometric sequence $\{b_n\}$ with a common ratio greater than 0, such that $b_1 = -2a_1 = 2$, $a_3 + b_2 = -1$, and $S_3 + 2b_3 = 7$.  
(Ⅰ) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) Let $c_n = \frac{(-1)^{n-1}a_n}{b_n}$, find the sum of the first $n$ terms of sequence $\{c_n\}$, denoted as $T_n$.

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