
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
There are three interest groups $A$, $B$, and $C$ with 5, 4, and 7 members respectively. There are 3 members participating in both groups $A$ and $B$, and 2 members participating in groups $A$, $B$, and $C$ simultaneously. Let the number of members in $(A \cup B) \cap C$ be $x$, and the number of members in $A \cup B \cup C$ be $y$. Find the range of values for $x$ and $y$.

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