
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 $\{a_n\}$, where $a_1=-60$ and $a_{17}=-12$.

$(1)$ From which term does the sequence become positive?  
$(2)$ For how many initial terms is the sum minimal? Find the minimal value of the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$.  
$(3)$ Let $T_n=|a_1|+|a_2|+|a_3|+\ldots+|a_n|$.

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