
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 following 3 propositions: ① If $a, b \in \mathbb{R}$, then $\frac{a+b}{2} \geq \sqrt{ab}$; ② If $x \in \mathbb{R}$, then $x^2+1 > x$; ③ If $x \in \mathbb{R}$ and $x \neq 0$, then $x + \frac{1}{x} \geq 2$. Among these, the true proposition number is __________.

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