
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
Let the sum of the first $n$ terms of a geometric sequence $\{a_n\}$ with a common ratio greater than zero be $S_n$, and $a_1=1$, $S_4=5S_2$. The sum of the first $n$ terms of the sequence $\{b_n\}$ is $T_n$, satisfying $b_1=1$, $$T_{n}=n^{2}b_{n}$$, where $n\in\mathbb{N}^{*}$.  
(Ⅰ) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) Let $C_n=(S_n+1)(nb_n-\lambda)$. If the sequence $\{C_n\}$ is a monotonically decreasing sequence, find the range of values for the real number $\lambda$.

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