
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 $\{a\_n\}$ with the sum of the first $n$ terms denoted as $S\_n$. It is known that $S\_5 = 5S\_2$ and $2a\_1 + 1 = a\_3$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $\{b\_n\} = \frac{1}{a\_n a\_{n+1}}\}$. Find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{b\_n\}$.

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