
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
In the sequence $\{a\_n\}$, $a\_1=2$, and the points $(a\_n,a_{n+1}) (n∈N^{})$ are on the line $y=2x$.

(1) Find the general term formula of the sequence $\{a\_n\}$.

(2) If $b\_n=\log _{2}a_{n}$, find the sum of the first $n$ terms, $T_{n}$, of the sequence $\left\{\dfrac{1}{b_{n}·b_{n+1}} \right\}$.

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