
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 that the first term of the positive sequence {$a_n$} is 1 and satisfies $$\frac {a_{n+1}-2}{a_{n}}= \frac {a_{n}+2}{a_{n+1}},\ b_{n}= \frac {3×2^{a_{n}}}{(2^{a_{n+1}}-1)(2^{a_{n}}-1)}$$, let $T_n$ denote the sum of the first $n$ terms of the sequence {$b_n$}. If λ is less than or equal to $$\frac {1}{32(1-T_{n})}+ \frac {32}{2^{a_{n+1}}}$$ for any $n \in \mathbb{N}^*$, determine the range of values for the real number λ.

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