
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
In the arithmetic sequence ${a_n}$, ${a_1=8,a_3=4}$.

(1) Let the sum of the first $n$ terms of the sequence ${a_n}$ be ${S_n}$. Find the maximum value of ${S_n}$ and the value of $n$ that makes ${S_n}$ maximum.

(2) Let ${b_n=\frac{1}{n(12-{a_n})}\ (n\in\mathbb{N}^*)}$. Find ${T_n=b_1+b_2+...+b_n\ (n\in\mathbb{N}^*)}$.

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