
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 circular park consists of an outer-ring path for walkers (white), a ring-shaped flower garden (gray) surrounding a central circular fountain (black). The walking path is six feet wide at all points, the garden ring is now ten feet wide at all points, and the fountain has a diameter of 12 feet. What is the radius, in feet, of the circle that forms the outer boundary of the flower garden?

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