
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 sets $S$ and $T$ that satisfy $S⊆T$ and $S≠∅$, if $S$ meets the following conditions:

(i) $∀a, b∈S$, it follows that $a-b∈S$ and $ab∈S$;

(ii) $∀r∈S, n∈T$, it follows that $rn∈S$.

Then $S$ is called an ideal of $T$, denoted as $S < T$.

Among the following three pairs of sets:

1. $S={0}$, $T=R$;
2. $S={$even numbers$}$, $T=Z$;
3. $S=R$, $T=C$,

Find the serial numbers of the pairs that satisfy $S < T$ (write down all the serial numbers you think are correct).

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