
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 $\{a_n\}$ is an arithmetic sequence satisfying $a_1=2$ and $a_4=14$, and the sequence $\{b_n\}$ satisfies $b_1=1$ and $b_4=6$, and $\{a_n-b_n\}$ is a geometric sequence.

(Ⅰ) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.

(Ⅱ) If for all $n \in \mathbb{N}^*$, $b_n \leqslant b_k$ holds, find the value of the positive integer $k$.

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