
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 point \( M_0 \) to the plane passing through three points \( M_1 \), \( M_2 \), and \( M_3 \).

Given points:

\( M_1(1, 1, 2) \)

\( M_2(-1, 1, 3) \)

\( M_3(2, -2, 4) \)

\( M_0(2, 3, 8) \)

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