
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 $D$ be the circle with equation $x^2 - 8x + y^2 + 10y = -14$. A translation of the coordinate system moves the center of $D$ to $(1, -2)$. Determine $a+b+r$ after the translation, where $(a,b)$ is the center and $r$ is the radius of the translated circle.

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