
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
(Physics) Let $S$ be a non-empty subset of the set of integers $Z$. If for all $a, b \in S$, we have $ab \in S$, then $S$ is said to be closed under multiplication. Suppose $T$ and $V$ are two non-empty subsets of $Z$ that do not intersect, and $T \cup V = Z$, and for all $a, b, c \in T$, we have $abc \in T$, and for all $x, y, z \in V$, we have $xyz \in V$. The conclusions are:  
① At least one of $T$ and $V$ is closed under multiplication;  
② At most one of $T$ and $V$ is closed under multiplication;  
③ Exactly one of $T$ and $V$ is closed under multiplication;  
④ Each of $T$ and $V$ is closed under multiplication.  
Among these conclusions, the one that always holds is $ \boxed{\text{①}}$.

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