
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 $\{a_n\}$ is an increasing arithmetic sequence, and $a_2$, $a_3$ are the roots of the equation $x^2-8x+15=0$.

(Ⅰ) Find the general formula for $\{a_n\}$;

(Ⅱ) Calculate the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{{a_n}\cdot {a_{n+1}}} \right\}$.

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