
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
Points \( K \) and \( M \) are the midpoints of the edges \( AB \) and \( AC \) of the triangular pyramid \( ABCD \) with a base area \( p \). Find the area of face \( BCD \), given that the cross-section \( DKM \) has an area \( q \), and the base of the pyramid's height falls on the intersection of the medians of the base triangle \( ABC \).

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