
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
Swiss mathematician Euler proposed in his book "Geometry of Triangles" in 1765 that the circumcenter, centroid, and orthocenter of any triangle lie on the same line, which is later known as the Euler line. Given the vertices $A(-4,0)$, $B(0,4)$, and $C(2,0)$ of triangle $\triangle ABC$, find the equation of the Euler line of $\triangle ABC$.

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