
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 standard domino game consists of 28 tiles. Each tile is made up of two integers ranging from 0 to 6, inclusive. All possible combinations $(a, b)$, where $a \leq b$, are listed exactly once. Note that tile $(4,2)$ is listed as tile $(2,4)$, because $2 \leq 4$. Excluding the piece $(0,0)$, for each of the other 27 tiles $(a, b)$, where $a \leq b$, we write the fraction $\frac{a}{b}$ on a board.

a) How many distinct values are written in the form of fractions on the board? (Note that the fractions $\frac{1}{2}$ and $\frac{2}{4}$ have the same value and should be counted only once.)

b) What is the sum of the distinct values found in the previous item?

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