
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 a common difference $d \neq 0$, $S_7=35$, and $a_2$, $a_5$, $a_{11}$ form a geometric sequence.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Let $T_n$ be the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{a_na_{n+1}} \right\}$, and there exists $n \in \mathbb{N}^*$ such that $T_n - \lambda a_{n+1} \geqslant 0$ holds, find the range of the real number $\lambda$.

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