
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
Points \( A \) and \( B \) lie in the plane \( \alpha \). Let \( M \) be a point in space such that \( AM = 2 \), \( BM = 5 \), and the orthogonal projection of segment \( BM \) onto the plane \( \alpha \) is three times the orthogonal projection of segment \( AM \) onto this plane. Find the distance from point \( M \) to the plane \( \alpha \).

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