
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 quadratic function $y=f(x)$ ($x \in \mathbb{R}$) whose graph passes through the point $(0,-3)$, and the solution set for $f(x) > 0$ is $(1,3)$.
(1) Find the expression for $f(x)$.
(2) Determine the maximum and minimum values of the function $y=f(\sin x)$, where $x \in \left[0, \frac{\pi}{2}\right]$.

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