
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
For a given sequence $\{c_n\}$, if there exist real constants $p$ and $q$ such that $c_{n+1} = pc_n + q$ holds for any $n \in \mathbb{N}^*$, we call the sequence $\{c_n\}$ an "M-type sequence".
(1) If $a_n = 2n$ and $b_n = 3 \cdot 2^n$ for $n \in \mathbb{N}^*$, are the sequences $\{a_n\}$ and $\{b_n\}$ "M-type sequences"? If yes, specify the corresponding real constants $p$ and $q$; if not, please explain why.
(2) If the sequence $\{a_n\}$ satisfies $a_1 = 2$ and $a_n + a_{n+1} = 3 \cdot 2^n$ for $n \in \mathbb{N}^*$:
① Find the sum of the first 2015 terms of the sequence $\{a_n\}$;
② Given that the sequence $\{a_n\}$ is an "M-type sequence", find $a_n$.

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