
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. Point \(P\) is the midpoint of arc \(EF\) of this semicircle. The length of the diameter \(EF\) is 10 centimeters. What is the length of line segment \(PG\)? Express your answer in simplest radical form.

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