
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
Given that the origin of the coordinate system is O, and the perpendicular line to the line 2mx - (4m + n)y + 2n = 0 (where m and n are not simultaneously zero) passes through point P(2, 6) with foot of the perpendicular M, find the range of values for |OM|.

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