
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 the function $f(x)$ is a logarithmic function, and its graph passes through the point $(2\sqrt{2}, \frac{3}{2})$, $g(x) = [f(x)]^2 - 2bf(x) + 3$, where $b \in \mathbb{R}$.
(1) Find the analytical expression of the function $f(x)$;
(2) Find the minimum value of the function $y=g(x)$ in the interval $[\sqrt{2}, 16]$.

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