
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 $\left\{a_{n}\right\}$ is a monotonically increasing arithmetic sequence, $a_{2}+a_{4}=14$, and $a_{2}-1$, $a_{3}+1$, $a_{4}+7$ form a geometric sequence.

(1) Find the general formula for the sequence $\left\{a_{n}\right\}$.

(2) Let the sum of the first $n$ terms of the sequence $\left\{\dfrac{6}{a_{n}a_{n+1}}\right\}$ be $S_{n}$.

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