
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
In an arithmetic sequence $\{a_n\}$ with a non-zero common difference, $a_1=2$ and $a_1$, $a_2$, $a_4$ form a geometric sequence.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) Let $b_n=(-1)^{n+1}\left( \frac{2}{a_n}+ \frac{2}{a_{n+1}}\right)$, find the sum of the first $2n-1$ terms of the sequence $\{b_n\}$, denoted as $T_{2n-1}$.

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