
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
Letters $A, B, C,$ and $D$ represent four different digits selected from $0,1,2, \ldots, 9.$ The fraction $\frac{A+B}{C+D}$ must be an integer and as large as possible. Additionally, the sum of digits $C + D$ must be at least $5$. What is the optimal value of $A+B$ under these conditions?
A) 12
B) 13
C) 14
D) 15
E) 16

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