
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
In the  $xOy$  system consider the lines  $d_1\ :\ 2x-y-2=0,\ d_2\ :\ x+y-4=0,\ d_3\ :\ y=2$  and  $d_4\ :\ x-4y+3=0$ . Find the vertices of the triangles whom medians are  $d_1,d_2,d_3$  and  $d_4$  is one of their altitudes.

*Lucian Dragomir*

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