
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
On a line, points $A$, $B$, $C$, and $D$ are marked 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 $BC = 20$.

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