
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 triangle $ABC$, the coordinates of point $A$ and point $B$ are $(-1,2)$ and $(4,3)$, respectively. The midpoint $M$ of $AC$ lies on the y-axis, and the midpoint $N$ of $BC$ lies on the x-axis.
1. Find the coordinates of point $C$.
2. Find the equation of the line $MN$.

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