
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 a ray of light is emitted from point $A(-3,-1)$ and is reflected by the line $l: x-y-1=0$ and then passes through point $B(-4,4)$, let the reflection point be $C$.

$(1)$ Find the coordinates of point $C$;

$(2)$ Find the area of $\triangle ABC$.

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