
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 $y=f(x)$ is a quadratic function, and $y=f(x)$ attains its minimum value of $-4$ at $x=2$, and the graph of $y=f(x)$ passes through the origin.

(1) Find the expression for $f(x)$.
(2) Find the maximum and minimum values of the function $y=f\left(\log_{\frac{1}{2}} x\right)$ in the interval $\left[\frac{1}{8}, 2\right]$.

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