
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
A semicircle is constructed with a diameter $AB$ of length 10 centimeters. A square $ABCD$ is placed such that its side $AB$ coincides with the diameter of the semicircle. A point $N$ is the midpoint of arc $AB$. If another point $P$ is placed on segment $CD$ such that $CP:PD = 1:3$, what is the length of segment $NP$?

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