
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 monotonically increasing arithmetic sequence with the first term $a_1=3$ and the sum of the first $n$ terms denoted as $S_n$, and $\{b_n\}$ is a geometric sequence with the first term $b_1=1$ and such that $a_2b_2=12$ and $S_3+b_2=20$.

(Ⅰ) Find the general formulas for $\{a_n\}$ and $\{b_n\}$.
(Ⅱ) Let $C_n=n\cdot b_n$ for $n\in\mathbb{N}^+$, find the sum of the first $n$ terms of $\{c_n\}$, denoted as $T_n$.

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