
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 $PQR,$ the midpoint of $\overline{QR}$ is $(2,3,-1),$ the midpoint of $\overline{PR}$ is $(1,2,-2),$ and the midpoint of $\overline{PQ}$ is $(3,1,4).$ Find the coordinates of vertex $P.$

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