
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 the function $f(x)= \begin{cases} 1,x{\text{ is rational}}\\ 0,x{\text{ is irrational}} \end{cases}$, there are four propositions:

1. For any $x∈R$, $f(f(x))=1$;
2. The function $f(x)$ is an even function;
3. If $T$ is a non-zero rational number, then $f(x+T)=f(x)$ holds for any $x∈R$;
4. There are three points $A$, $B$, $C$ on the graph of $f(x)$ such that $△ABC$ is an equilateral triangle.

The sequence number of the correct propositions is _______.

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