
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

In the triangular pyramid \( PABC \), the side edge \( PB \) is perpendicular to the base plane \( ABC \), \( PB = 6 \), \( AB = BC = \sqrt{15} \), \( AC = 2\sqrt{3} \). A sphere with center \( O \), which lies on the face \( ABP \), touches the planes of the other faces of the pyramid. Find the distance from the center \( O \) of the sphere to the edge \( AC \).

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