
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 tetrahedron \(EFGH\), it is given that \(EF = GH = 7\), \(EG = FH = 10\), and \(EH = FG = 11\). The points \(K, L, M, N\) are the centers of the circles inscribed in the triangles \(EFG\), \(EFH\), \(EGH\), and \(FGH\) respectively. Find the volume of the tetrahedron \(KLMN\). If necessary, round your answer to the nearest hundredth.

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