
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 an arithmetic sequence $\{a_n\}$, the sum of the first $n$ terms is $S_n$, the common difference $d \neq 0$, and $S_3 + S_5 = 58$. Also, $a_1$, $a_3$, and $a_7$ form a geometric sequence.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) If $\{b_n\}$ is a geometric sequence, and $b_5 \cdot b_6 + b_4 \cdot b_7 = a_8$, denote $T_n = \log_3 b_1 + \log_3 b_2 + \ldots + \log_3 b_n$, find the value of $T_{10}$.

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