
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
Suppose you have a large piece of cookie dough, shaped into a circle with a radius of $5$ inches. From this dough, three cookies each of radius $1$ inch and four cookies each of radius $0.5$ inch have been cut out. All cookies are tangent, and all except the center cookie are tangent to the edge of the dough. Any leftover scrap is reshaped to form another cookie of the same thickness. What is the radius of this scrap cookie?
A) $\sqrt{10}$
B) $\sqrt{15}$
C) $\sqrt{20}$
D) $\sqrt{21}$
E) $\sqrt{25}$

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