
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 large circular piece of cookie dough with a radius of 5 inches from which eight smaller cookies, each with a radius of 1 inch, are cut, and the leftover scrap dough is reformed into another cookie of the same thickness, determine the radius of the cookie made from the leftover scrap dough.

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