
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 $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$. The first term $a_1=2$, and all terms are positive ($a_n > 0, n\in \mathbb{N}^*$). It is known that $S_6 + a_6$ is the middle term of the arithmetic sequence formed by $S_4 + a_4$ and $S_5 + a_5$.

(1) Find the general term formula for the sequence $\{a_n\}$.

(2) Let $b_n=\log_{\frac{1}{2}}{(a_{2n-1})}$. If the sum of the first $n$ terms of the sequence $\{\frac{2}{b_nb_{n+1}}\}$ is denoted as $T_n$, find $T_n$.

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