
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 $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, the point $(a_{n}+2, S_{n+1})$ lies on the line $y=4x-5$, where $n \in \mathbb{N}^*$. Let $b_n = a_{n+1} - 2a_n$, and $a_1 = 1$. Find the general formula for the sequence $\{b_n\}$; if $f(x) = b_1x + b_2x^2 + b_3x^3 + \ldots + b_nx^n$, calculate the result of $f′(1)$.

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