
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 triangle $ABC,$ the midpoint of $\overline{BC}$ is $(2,6,-2),$ the midpoint of $\overline{AC}$ is $(1,5,-3),$ and the midpoint of $\overline{AB}$ is $(3,4,5).$ Find the coordinates of vertex $A$ and verify if the centroid of the triangle is at $(2,5,0).$

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