
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 \( A, B, C, \) and \( D \) are marked on a line in that order. Point \( M \) is the midpoint of segment \( AC \), and point \( N \) is the midpoint of segment \( BD \). Find the length of segment \( MN \) if it is known that \( AD = 68 \) and \( BC = 26 \).

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