
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 pyramid \(ABCD\), the lengths of edges \(AB\) and \(CD\) are each 4, and the lengths of all other edges are each 3. A sphere is inscribed in this pyramid. Find the volume of the pyramid whose vertices are the points of tangency of the sphere with the faces of the pyramid \(ABCD\).

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