
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 volume of a tetrahedron and a pyramid

A convex polyhedron \(ABCDEF\) has five faces: \(CDF\), \(ABE\), \(BCFE\), \(ADF E\), and \(ABCD\). Edge \(AB\) is parallel to edge \(CD\). Points \(K\) and \(L\) are located on edges \(AD\) and \(BC\), respectively, such that segment \(KL\) divides the area of face \(ABCD\) in half. Point \(M\) is the midpoint of edge \(EF\) and is the apex of the pyramid \(MABCD\), whose volume is 6. Find the volume of pyramid \(EKLF\) if the volume of polyhedron \(ABCDEF\) is 19.

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