
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 propositions are given:
① Given $a$ and $b$ are both positive numbers, and $$\frac {a+1}{b+1} > \frac {a}{b}$$, then $a < b$.
② Given $f'(x)$ is the derivative of $f(x)$, if for all $x \in \mathbb{R}$, $f'(x) \ge 0$, then it must be true that $f'(1) < f(2)$.
③ The negation of the proposition "There exists an $x \in \mathbb{R}$ such that $x^2 - 2x + 1 < 0$" is true.
④ $x \le 1$ and $y \le 1$ are necessary and sufficient conditions for "$x + y \le 2$".
⑤ Converting the decimal number $23_{(10)}$ into binary representation yields $10111_{(2)}$.
⑥ A student investigating the correlation between variables $x$ and $y$ derived the regression line equation and concluded that $y$ is positively correlated with $x$ and $$\hat y = -4.326x - 4.5$$. Identify the correct proposition numbers.

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