
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 f(x) = x^2 - x + b, f(log₂a) = b, and log₂f(a) = 2 (where a > 0 and a ≠ 1),

1. Find the values of a and b.
2. Find the minimum value of f(log₂x) and the corresponding value of x.

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