
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
For the function $f(x)$, the solution to the equation $f(x) = x$ is called the fixed point of $f(x)$, and the solution to the equation $f(f(x)) = x$ is called the stable point of $f(x)$.  
① Let the set of fixed points of the function $f(x)$ be $M$, and the set of stable points be $N$, then $M \subseteq N$;  
② The function $f(x)$ can have infinitely many stable points;  
③ When $f(x)$ is monotonically increasing in its domain, if $x_0$ is a stable point of $f(x)$, then $x_0$ is a fixed point of $f(x)$;  
Among the above three propositions, the serial numbers of all true propositions are __________.

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