
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 $\{a\_n\}$ with its first $n$ terms sum $S\_n$, where $a\_1=1$, $a_{n+1}=λS\_n+1 (n∈N^*, λ > 0)$, and $a\_1$, $a\_2+2$, $a\_3+3$ form an arithmetic sequence.
(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Let $b\_n=(-1)^{n}\log \_2a\_n \cdot \log \_2a_{n+1}$, find the sum $T_{2n}$ of the first $2n$ terms of the sequence $\{b\_n\}$.

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