
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 geometric sequence $\{a_n\}$ with a common ratio $q > 1$, $a_1 = 2$, and $a_1, a_2, a_3 - 8$ form an arithmetic sequence. The sum of the first n terms of the sequence $\{b_n\}$ is denoted as $S_n$, and $S_n = n^2 - 8n$.
(I) Find the general term formulas for both sequences $\{a_n\}$ and $\{b_n\}$.
(II) Let $c_n = \frac{b_n}{a_n}$. If $c_n \leq m$ holds true for all $n \in \mathbb{N}^*$, determine the minimum value of the real number $m$.

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