
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 points $A(-4,0)$, $B(0,3)$, $\triangle ABC$ is an isosceles triangle with $AB\perp BC$. <br/>$(1)$ Find the coordinates of point $C$; <br/>$(2)$ Find the equation of the line containing the median of side $AC$.

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