
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 four terms $S_4=14$, and $a_1$, $a_3$, $a_7$ form a geometric sequence.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Let $T_n$ be the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{a_na_{n+1}} \right\}$, if $T_n \leqslant \lambda a_{n+1}$ holds for $\forall n \in \mathbb{N}^*$, find the minimum value of the real number $\lambda$.

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