
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 $\{a_n\}$ is an arithmetic sequence with $a_1=13$ and $a_4=7$,
1. Find the general formula for $\{a_n\}$.
2. Find the sum of the first $n$ terms of $\{a_n\}$ denoted as $S_n$, and determine the maximum value of $S_n$ and the corresponding term.
3. Calculate the sum of the absolute values of the first $n$ terms of the sequence, denoted as $T_n$.

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