
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
Point \( M \) lies inside the segment \( AB \), whose length is 40 cm. Points are chosen as follows: \( N \) is at the midpoint of \( AM \), \( P \) is at the midpoint of \( MB \), \( C \) is at the midpoint of \( NM \), and \( D \) is at the midpoint of \( MP \). Find the length of the segment \( CD \) in cm.

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