
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 bear stumbled upon a berry circle with the boundary given by the equation $x^2+y^2 - 12 = 2x + 4y$. He wonders if the area of this berry circle is enough for him to have a full meal. What is the radius of this berry circle and is the area larger than 30 square units?

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