
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 points \( A_1 (x_1 , y_1 , z_1 ), A_2 (x_2 , y_2 , z_2 ), \ldots , A_n (x_n , y_n , z_n ) \), let \( P (x, y, z) \) be the point which minimizes \( \sum ( |x - x_i | + |y - y_i | + |z - z_i | ) \). Give an example (for each \( n > 4 \)) of points \( A_i \) for which the point \( P \) lies outside the convex hull of the points \( A_i \).

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