
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 its first $n$ terms denoted as $S\_n$, it is known that $a\_5+a\_6=24$ and $S_{11}=143$. Another sequence $\{b\_n\}$ has the sum of its first $n$ terms denoted as $T\_n$, and it satisfies the equation $2^{a\_n-1}=λT\_n-(a\_1-1)$, where $n∈ℕ^*$.

(I) Find the general term formula for the sequence $\{a\_n\}$ as well as the sum of the first $n$ terms for the sequence $\{ \frac {1}{a\_n a_{n+1}} \}$.
(II) Determine whether there exists a non-zero real number $λ$ such that the sequence $\{b\_n\}$ is a geometric sequence, and provide a rationale for your answer.

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