
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

Find the distance from the point \(M_{0}\) to the plane that passes through the three points \(M_{1}, M_{2}, M_{3}\).

\(M_{1}(-2 ; 0 ;-4)\)

\(M_{2}(-1 ; 7 ; 1)\)

\(M_{3}(4 ;-8 ;-4)\)

\(M_{0}(-6 ; 5 ; 5)\)

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