
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 the coordinates of the three vertices of $\Delta ABC$ are $A(-1,1)$, $B(7,-1)$, and $C(-2,5)$, and the line containing the median from vertex $A$ to side $BC$ is $l$.

$(1)$ Find the equation of line $l$;

$(2)$ If the point $A$ is symmetric to point $D$ with respect to line $l$, find the area of $\Delta BCD$.

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