
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]


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Given an arithmetic sequence ${{a_{n}}}$ with a common ratio $q > 1$, ${{a_{1}}=1}$ and ${{a_{1}},{{a_{3}},{{a_{2}}+14}}}$ forms an arithmetic sequence. The sequence ${{a_{n}}}$ satisfies ${{a_{1}}{{b_{1}}+{{a_{2}}{{b_{2}}}+{{a_{3}}{{b_{3}}}+ \cdots +{{a_{n}}{{b_{n}}}=(n-1)} \cdot {{3^{n}}}+1,n\in N^{*}}}}$.

(1) Find the general terms of the sequences ${{a_{n}}}$ and ${{b_{n}}}$.
(2) If $m{{a_{n}}}\geqslant {{b_{n}}-8}$ always holds true, find the minimum value of the real number $m$.

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