
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 what ratio does the point \( P \) divide the perpendicular segment dropped from vertex \( A \) of a regular tetrahedron \( ABCD \) to the face \( BCD \), given that the lines \( PB \), \( PC \), and \( PD \) are mutually perpendicular to each other?

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