
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 the tetrahedron $V-ABC$, the three lateral edges are mutually perpendicular. Point $M$ is on the base $\triangle ABC$, and the distances from $M$ to each of the three lateral faces are $2\text{ cm}$, $3\text{ cm}$, and $6\text{ cm}$, respectively. Find the distance from point $M$ to the apex $V$ of the tetrahedron.

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