
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 $\triangle ABC$ are $A(-1, 1)$, $B(7, -1)$, and $C(-2, 5)$, and the line of the median on side $AB$ is $l$.
(1) Find the equation of line $l$;
(2) If the symmetric point of $A$ with respect to line $l$ is $D$, find the area of $\triangle BCD$.

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