
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
In the Cartesian coordinate system, given that the coordinates of the three vertices of triangle ABC are $A(-1,2)$, $B(-3,4)$, and $C(0,6)$.  
$(1)$ Find the equation of the line containing the altitude on side $BC$.  
$(2)$ Find the area of triangle ABC.

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