
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 pyramid \( DABC \) has a triangular base (see Fig. 5). Given that \( \overline{AK} = \overline{KD} \), \( \overline{BP} = \overline{PC} \), and \( \overline{DM} = 0.4 \cdot \overline{DC} \). Find the area \( S \) of the cross-section of the pyramid created by the plane \( KMP \), if the vertex \( A \) is at a distance \( h = 1 \) from the plane \( KMP \), and the volume of the pyramid \( DABC \) is equal to 5.

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