
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
The side length of an equilateral triangle ABC is 8, and there is a point O in the plane of ∆ABC satisfying $\overrightarrow{OA} - 2\overrightarrow{OB} - 3\overrightarrow{OC} = \overrightarrow{0}$. If M is a point on the side of ∆ABC and point P satisfies |OP| = √19, determine the maximum value of |MP|.

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