
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 geometric sequence $\{a_n\}$ with a common ratio $q > 0$, whose sum of the first $n$ terms is $S_n$, and given $a_{1}=1$ and $S_{3}=7$, along with a sequence $\{b_n\}$ where $b_{1}=0$, and $b_{3}=1$:

(Ⅰ) If the sequence $\{a_n + b_n\}$ forms an arithmetic sequence, find $a_n$ and $b_n$;

(Ⅱ) Under the condition of (Ⅰ), find the sum of the first $n$ terms $T_n$ of the sequence $\{b_n\}$.

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