
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-geometric sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, it satisfies the equation $2S\_n = 2^{n+1} + λ (λ ∈ R)$.

(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) If sequence $\{b\_n\}$ satisfies $b\_n = \frac{1}{(2n+1)\log\_4(a\_na\_n+1)}$, find the sum of the first $n$ terms of sequence $\{b\_n\}$, denoted as $T\_n$.

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