
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
The three vertices of $\triangle ABC$ are $A(4,0)$, $B(6,7)$, $C(0,3)$. Find:<br/>
$(1)$ The equation of the median on side $BC$;<br/>
$(2)$ The equation of the altitude on side $BC$.

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