
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
Let the function \( f(x) \) satisfy \( f\left(2^{x}\right)=x^{2}-2ax+a^{2}-1 \), and the range of \( f(x) \) over the interval \(\left[2^{a-1}, 2^{a^{2}-2a+2}\right]\) is \([-1, 0]\). Determine the range of values for \( a \).

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