
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 the function f(x) = $\frac{2}{3}$($\frac{2^x}{2^x - 1}$ + b), where b ∈ R, is an odd function in its domain, and the function g(x) = log<sub>2</sub>[(a - 1)x² - 2x + 1], where a ∈ R.
(1) Find the value of b.
(2) If there exists x₁ ∈ [1, 2] such that for any x₂ ∈ [1, 2], f(x₁) ≥ g(x₂) holds true, find the range of values for the real number a.

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