
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 distinct terms, the sum of the first five terms $S\_5=20$, and $a\_1$, $a\_3$, $a\_7$ form a geometric sequence.
(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) Let $T\_n$ be the sum of the first $n$ terms of the sequence $\{\frac{1}{a\_n a\_{n+1}}\}$. If there exists $n \in \mathbb{N}^*$ such that $T\_n - \lambda a\_{n+1} \geq 0$, find the range of values for the real number $\lambda$.

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