
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 four points  $A(-1,2), B(3,-4), C(5,-6),$  and  $D(-2,8)$  lie in the coordinate plane. Compute the minimum possible value of  $PA + PB + PC + PD$  over all points P .

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