
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 the vertices $A(-2,4)$, $B(4,-6)$, $C(5,1)$ of triangle $\triangle ABC$.
$(1)$ Find the equation of the median on side $AB$.
$(2)$ Find the equation of the line passing through point $A$ with intercepts on the $x$-axis and $y$-axis being equal.

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