
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 $\{a_n\}$ is a geometric sequence with all positive terms, and $a_1 + a_2 = 6$, $a_1a_2 = a_3$.

(Ⅰ) Find the general formula for the sequence $\{a_n\}$;

(Ⅱ) Let $\{b_n\}$ be a non-zero arithmetic sequence with the sum of the first $n$ terms denoted as $S_n$. Given that $S_{2n+1} = b_nb_{n+1}$, find the sum of the first $n$ terms, $T_n$, for the sequence $\left\{ \frac{b_n}{a_n} \right\}$.

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