
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
An elf attempts to reformulate the shape of magic summoning circle originally defined by the equation $$x^2 - 6x + y^2 - 10y + 18 = 0.$$ The elf wishes to mold this into a perfect circular form with center (h, k) and radius r such that the equation becomes $$(x-h)^2 + (y-k)^2 = r^2.$$ What are the values of h, k, and r?

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