
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 $\{a\_n\}$, the sum of its first $n$ terms is $S\_n$. It is known that $a\_{22} - 3a\_7 = 2$ and $\frac{1}{a\_2}, \sqrt{S\_2 - 3}, S\_3$ form a geometric sequence. Let $b\_n = \frac{4(n+1)}{a\_n^2 a\_{n+2}^2}$ and the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $T\_n$. For any positive integer $n$, if $64T\_n < |3λ - 1|$ holds, find the range of the real number $λ$.

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