
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 distance from the center \( O \) of a sphere with radius 12, which is circumscribed around a regular quadrangular pyramid, to a lateral edge is \( 4 \sqrt{2} \). Find: 
1) the height of the pyramid;
2) the distance from point \( O \) to the lateral face of the pyramid;
3) the radius of the sphere inscribed in the pyramid.

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