
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 $\{a_{n}\}$ that satisfies $\frac{a_1}{2}+\frac{a_2}{2^2}+⋯+\frac{a_n}{2^n}=n(n≤N^*)$, and $b_n=λ(a_n-1)-n^2+4n$. If the sequence $\{b_{n}\}$ is a monotonically increasing sequence, then the range of $\lambda$ is ______.

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