
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 the sequence $\{a\_n\}$ is an arithmetic sequence with a positive first term, and the sum of the first $n$ terms of the sequence $\{\frac{1}{a\_n a\_{n+1}}\}$ is $S\_n = \frac{n}{2n+1}$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) Let $b\_n = (-1)^n a_{n^2}$, find the sum of the first 20 terms of the sequence $\{b\_n\}$, denoted as $T_{20}$.

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