
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 the sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n$, and it satisfies $a_n > 0$, $S_n = \frac{1}{4}(a_n + 1)^2$. The sequence $\{b_n\}$ satisfies $b_1 = 1$, $\frac{b_{n+1}}{b_n} = \frac{2a_n}{a_{n+1}}$.
(I) Find the general terms of the sequences $\{a_n\}$ and $\{b_n\}$;
(II) If for all $n \in \mathbb{N}^*$, $\lambda > \frac{1}{b_1} + \frac{1}{b_2} + \dots + \frac{1}{b_n}$ always holds, find the minimum value of the real number $\lambda$.

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