
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 that $a, b \in R^{+}$, determine the correct proposition(s) from the following:

$①$ If $a^{2}-b^{2}=1$, then $a-b < 1$;

$②$ If $\frac{1}{b} - \frac{1}{a} = 1$, then $a-b < 1$;

$③$ If $|\sqrt{a} - \sqrt{b}| = 1$, then $|a-b| < 1$;

$④$ If $|a^{2}-b^{2}| = 1$, then $|a-b| < 1$.

The sequence number of the correct proposition(s) is $\_\_\_\_\_\_\_\_$.

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