
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 graph of the quadratic function $y=x^{2}-2x-3$ intersects the $x$-axis at points $A$ and $B$ (with point $A$ to the left of point $B$) and point $C$ is the vertex of the parabola.  
$(1)$ Find the coordinates of the intersection points of the graph of this quadratic function with the $x$-axis.  
$(2)$ Find the perimeter of $\triangle ABC$.

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