
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
Let \(ABCD\) be a quadrilateral with \(A = (3,4)\), \(B = (9, -40)\), \(C = (-5, -12)\), and \(D = (-7, 24)\). Let \(P\) be a point in the plane (not necessarily inside the quadrilateral). Find the minimum possible value of \(AP + BP + CP + DP\).

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