
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 circle of radius $r$ passes through both foci of, and exactly four points on, the ellipse with equation $4x^2+9y^2=36.$ Calculate the set of all possible values of $r$ is an interval $[a,b).$ What is $a+b?$
A) $\sqrt{5} + 6$
B) $8$
C) $12$
D) $\sqrt{5} + 7$

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