
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]


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Given a sequence $\{a_n\}$, the sum of its first $n$ terms $S_n$ satisfies $S_{n+1} = 2\lambda S_n + 1$ (where $\lambda$ is a constant greater than 0), and $a_1 = 1$, $a_3 = 4$.

(Ⅰ) Find the value of $\lambda$;  
(Ⅱ) Find the general formula for the sequence $\{a_n\}$.

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