
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
The following are three propositions:  
① If $|a-b|<1$, then $|a|<|b|+1$;  
② If $a, b \in \mathbb{R}$, then $|a+b|-2|a| \leq |a-b|$;  
③ If $|x|<2$, $|y|>3$, then $\left| \frac{x}{y} \right| < \frac{2}{3}$,  
Among these, the correct proposition numbers are __________.

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