
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 ${a_n}$, where $a_2a_6=64$, and $\log_2a_n$, $\frac{1}{2}\log_2a_{n+1}$, $1$ form an arithmetic sequence.

1. Find the general term formula for the sequence ${a_n}$.
2. If the sequence ${b_n}$ satisfies $b_n=\frac{a_n}{(a_n+1)(a_{n+1}+1)}$, and the sum of the first $n$ terms of the sequence ${b_n}$ is $T_n$, find $T_n$.

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