
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 $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$, $a_4=2$, and $S_{21}=-252$.
$(1)$ Find $a_n$ and $S_n$;
$(2)$ Let $T_n=|a_1|+|a_2|+\ldots+|a_n|$, find $T_n$.

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