
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 $\{a_n\}$, the sum of its first $n$ terms is $S_n$. If $S_{m-1}=-4$, $S_{m}=0$, $S_{m+2}=14$ ($m\geqslant 2$, $m\in\mathbb{N}^{\ast}$),
(1) Find the value of $m$;
(2) If the sequence $\{b_n\}$ satisfies $\frac{a_{n}}{2}=\log_{2}b_{n}$ ($n\in\mathbb{N}^{\ast}$), find the sum of the first $n$ terms of the sequence $\{(a_{n}+6)·b_{n}\}$.

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