
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 $\left\{ a_n \right\}$, $a_{15}+a_{16}+a_{17}=-45$, $a_{9}=-36$, and $S_n$ is the sum of the first $n$ terms.

(1) Find the minimum value of $S_n$ and the corresponding value of $n$;

(2) Calculate $T_n = \left| a_1 \right| + \left| a_2 \right| + \ldots + \left| a_n \right|$.

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