
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 the sequence $\{a\_n\}$ with the sum of its first $n$ terms $S\_n=10n-n^2 (n \in \mathbb{N}^*)$.

1. Find the general term formula for the sequence $\{a\_n\}$;
2. Find the maximum value of $S\_n$;
3. Let $b\_n = |a\_n|$, find the sum of the first 10 terms of the sequence $\{b\_n\}$, denoted as $T_{10}$.

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