
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 $\{a_n\}$, the sum of the first $n$ terms is $S_n$, and $S_n=2a_n-2$.
1. Find the general formula for the sequence $\{a_n\}$.
2. Let $b_n= \begin{cases} \frac {\log_{2}a_n}{n^2(n+2)}, & \text{if } n \text{ is odd} \\ \frac {2n}{a_n}, & \text{if } n \text{ is even} \end{cases}$, and $T_n$ be the sum of the first $n$ terms of $\{b_n\}$. Find $T_{2n}$.

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