
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 the sequence ${a_n}$ that satisfies $a_1=2$, $a_n=2^n\cdot a_{n-1}$ ($n\geq2$),
(1) Find the general formula for the sequence ${a_n}$;
(2) Let the sequence ${b_n}$ satisfy $b_n\cdot(\log_2 a_n)=1$, find the sum of the first $n$ terms of the sequence ${b_n}$, denoted as $T_n$.

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