
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
Ten cookies of radius 1 inch and one cookie of radius 2 inches are cut from a circle of cookie dough of radius 5 inches. All smaller cookies are tangent to at least another cookie or the edge of the dough, and they all surround the larger cookie, which is positioned in the center. The leftover scrap is reshaped to form another cookie of the same thickness. What is the radius in inches of the scrap cookie?
A) $\sqrt{7}$
B) $\sqrt{9}$
C) $\sqrt{11}$
D) $\sqrt{13}$
E) $\sqrt{15}$

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