
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 a sequence $\{a_n\}$ with $a_1=2$, and for $n \geq 2$, $a_n = 2a_{n-1} + 3 \cdot 2^{n-1}$,
(1) Find the formula for the sequence $\left\{\frac{a_n}{2^n}\right\}$ and the general term formula for the sequence $\{a_n\}$.
(2) Define $c_n = 2a_n - 3 \cdot 2^n$, and let $T_n$ be the sum of the first $n$ terms of the sequence $\{c_n\}$. Find $T_n$.

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