
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
Let $A = (4, 0, 0),$ $B = (0, -6, 0),$ $C = (0, 0, 8),$ and $D = (0, 0, -2).$ Find the point $P$ such that
\[AP = BP = CP = DP.\]

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