
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
Let $C$ be the circle with equation $x^2 - 4y - 36 = -y^2 + 12x + 16$. Find the values of $a$, $b$, and $r$ where $(a, b)$ is the center of $C$ and $r$ is its radius. What is $a + b + r$?

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