
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 the sum of the first $n$ terms being $S_n$, if $S_{m-1} = -4$, $S_m = 0$, $S_{m+2} = 14$ (where $m \geq 2$, and $m \in \mathbb{N^*}$),  
(1) Find the value of $m$;  
(2) If the sequence $\{b_n\}$ satisfies $\frac{a_n}{2} = \log_a b_n$ (where $n \in \mathbb{N^*}$), find the sum of the first $n$ terms of the sequence $\{(a_n + 6) \cdot b_n\}$.

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