
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 an arithmetic sequence $\{a\_n\}$ with a common ratio $q > 1$, $a\_1=1$, and $a\_1$, $a\_3$, $a\_2+14$ form an arithmetic sequence. The sequence $\{b\_n\}$ satisfies $a\_1b\_1+a\_2b\_2+…+a\_nb\_n=(n-1)⋅3^n+1$, $n∈N$.
(I) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) If $m a\_n ≥ b\_n - 8$ always holds, find the minimum value of the real number $m$.

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