
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
Set $X$ contains $30$ elements, and set $Y$ contains $25$ elements. It is known that at least $10$ elements are common to both sets, but not more than $20$ elements of set $Y$ are in set $X$. Determine the smallest possible number of elements in $X \cup Y$.

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