
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 an arithmetic sequence ${a_n}$, where $a_1=2$, $a_4=4a_6$.
1. Find the general term formula for the sequence ${a_n}$.
2. If $a_n>0$, let $b_n=-\log_2a_{2n+1}$, and the sum of the first $n$ terms of the sequence ${\frac{2}{b_nb_{n+1}}}$ is $T_n$, find $T_n$.

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