
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
Square $EFGH$ is constructed along diameter $EF$ of a semicircle, and both the semicircle and square $EFGH$ are coplanar. Line segment $EF$ has a length of 10 centimeters. If point $N$ is the midpoint of arc $EF$, what is the length of segment $NG$? Use the diagram given in the original problem with respective labels modified.

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