
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  $A$ ,  $B$ ,  $C$ ,  $D$  be four points on a circle in that order. Also,  $AB=3$ ,  $BC=5$ ,  $CD=6$ , and  $DA=4$ . Let diagonals  $AC$  and  $BD$  intersect at  $P$ . Compute  $\frac{AP}{CP}$ .

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