
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
Given a fraction $\frac{a}{b}$, not necessarily in the simplest form, such that $a$ and $b$ are positive integers and their sum is 20, determine the number of distinct integers that can be written as the sum of two, not necessarily different, such fractions.

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