
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
A square piece of cookie dough measures $6$ inches on each side. From this dough, four small cookies, each with a $1$ inch radius, and five smaller cookies, each with a radius of $0.5$ inches, are cut out. The leftover scrap is reshaped to form another cookie of the same thickness. Determine the radius in inches of this scrap cookie.

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