
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 a sequence ${a_n}$ with its sum of the first $n$ terms denoted as $S_n$, where $a_1=2$ and $S_n=(1-\frac{1}{2^n})a_{n+1}$. Let $b_n=\log_2a_n$, find the sum of the first $n$ terms, denoted as $T_n$, of the sequence ${\frac{1}{b_nb_{n+1}}}$.

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