
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 parabola $y=x^{2}+2x-3$ intersects the $y$-axis at point $C$ and the $x$-axis at points $A$ and $B$ where point $A$ is to the left of point $B.<br/>$(1)$ Write down the coordinates of points $A$, $B$, and $C$ directly;<br/>$(2)$ When $-3\leqslant x\leqslant 2$, find the difference between the maximum and minimum values of $y$.

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