
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 that the common difference of an arithmetic sequence $\{a_n\}$ (with the common difference not being zero) is $S$, and $S_5=20$, and that $a_1$, $a_3$, $a_7$ form a geometric sequence:

(I) Find the general formula for the sequence $\{a_n\}$;

(II) If $C_n = (2a_n - 4)n \cdot 3^{a_n - 2}$, find the sum of the first $n$ terms of the sequence $\{C_n\}$, $T_n$.

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