
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 the sequence $\{a_n\}$ that satisfies $a_{n+1} - a_n = 2^n (n \in \mathbb{N}^*)$, and $a_1 = 1$, let $b_n = a_n - 15n + 1 (n \in \mathbb{N}^*)$. Determine the minimum value of the sequence $\{b_n\}$.

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