
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
Let the sum of the first $n$ terms of the sequence $\{a_n\}$ be $S_n$, and the point $(n, \frac{S_n}{n})$, where $n \in \mathbb{N}^*$, all lie on the graph of the function $y=x$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) If $\{b_n\}$ is a geometric sequence, and $b_1 \neq 1$, $b_1b_2b_3 = 8$, find the sum of the first $n$ terms $T_n$ of the sequence $\{a_n + b_n\}$.

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