
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 base of a triangular pyramid is a triangle with sides \(a\), \(b\), and \(c\), and the lateral edges opposite these sides are \(m\), \(n\), and \(p\) respectively. Find the distance from the apex of the pyramid to the centroid of the base.

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