
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
Given a circle of cookie dough with a radius of $3$ inches, and seven smaller circles of radius $1$ inch are cut out from the larger circle in such a way that neighboring circles are tangent and all circles except the center one are tangent to the edge of the dough, determine the radius in inches of the leftover scrap cookie of the same thickness.

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