
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 barycentric coordinates of two points \(M\) and \(N\) are given as \(M\left(m_{1}, m_{2}, m_{3}\right)\) and \(N\left(n_{1}, n_{2}, n_{3}\right)\), respectively. What are the barycentric coordinates of the midpoint of the segment \(M N\)?

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