
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
In quadrilateral $ABCD,\ BC=10,\ CD=15,\ AD=12,$ and $m\angle A= m\angle B = 60^\circ.$ Given that $AB = r + \sqrt{s},$ where $r$ and $s$ are positive integers, find $r+s.$

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