
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
The mathematician Euler proposed a theorem in 1765: the circumcenter, centroid, and orthocenter of a triangle lie on the same line, and the distance from the centroid to the circumcenter is half the distance from the centroid to the orthocenter. This line is later known as the Euler line of the triangle. Given that the vertices of $\triangle ABC$ are $A(2,0)$, $B(0,4)$, and $AC=BC$, the equation of the Euler line of $\triangle ABC$ is \_\_\_\_\_\_ (expressed in the general form of the line equation).

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