
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 parabola $y=ax^2+bx+c$ passes through the points $(-1, 0)$, $(3, 0)$, and $(0, -3)$.
(1) Find the equation of this parabola and the coordinates of its vertex;
(2) If points $A(x_1, y_1)$ and $B(x_2, y_2)$ are on this parabola, and $x_1 < x_2 < 1$, compare the values of $y_1$ and $y_2$.

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