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

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