
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 \( A = (10, 0, 0) \), \( B = (0, -6, 0) \), \( C = (0, 0, 8) \), and \( D = (0, 0, 0) \). Find the point \( P \) such that 
\[ AP = BP = CP = DP. \]

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