
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 convex cyclic quadilateral. Suppose  $P$  is a point in the plane of the quadilateral such that the sum of its distances from the vertices of  $ABCD$  is the least. If   $$ \{PC, PB, PC, PD\} = \{3, 4, 6, 8\} $$  , what is the maxumum possible area of  $ABCD$ ?

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