
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 a right-angled triangle $\triangle ABC$ with vertex $A$ at coordinates $(-2, 0)$, the right-angle vertex $B$ at coordinates $(1, \sqrt{3})$, and vertex $C$ on the x-axis.  
(1) Find the equation of the line on which side $BC$ lies;  
(2) Find the equation of the line on which the median to the hypotenuse of $\triangle ABC$ lies.

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