
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 a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and it satisfies $S_n = (-1)^n \cdot a_n - \frac{1}{2^n}$. Define $b_n = 8a_2 \cdot 2^{n-1}$. If for any $n \in \mathbb{N}^*$, it always holds that $\lambda b_n - 1 > 0$, then the range of values for the real number $\lambda$ is __________.

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