
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 a function $f(2^x) = x^2 - 2ax + 3$,  
(1) Find the explicit expression for the function $y = f(x)$.  
(2) If the function $y = f(x)$ has a minimum value of -1 on the interval $\left[\frac{1}{2}, 8\right]$, find the value of $a$.

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