
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
(The full score of this question is 12 points)

Given that the graph of the function $f(x) = m \cdot 2^x + t$ passes through points $A(1,1)$, $B(2,3)$, and $C(n, S_n)$, where $S_n$ is the sum of the first $n$ terms of the sequence $\{a_n\}$, and $n \in \mathbb{N}^*$.

(1) Find $S_n$ and $a_n$;

(2) If the sequence $\{c_n\}$ satisfies $c_n = 6n \cdot a_n - n$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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