
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 $\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. Find all pairs of distinct two-digit numbers $(x, y)$ where $x < y$, such that $\clubsuit(x) = \clubsuit(y) = 6$.
A) 10
B) 13
C) 15
D) 17
E) 20

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