
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 sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and the sequence ${a_n}$ is an arithmetic sequence with $a_1=12$ and common difference $d=-2$.

(1) Find $S_n$

(2) Find the maximum (or minimum) term of ${S_n}$

(3) Find the largest $n$ such that $S_n$ is greater than zero.

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