
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
Among the following propositions, the incorrect ones are __________.  
① The converse of the proposition "If $x= \frac{\pi}{6}$, then $\sin x= \frac{1}{2}$" is true.  
② Let $a$, $b$ be real numbers, then $a<b$ is a sufficient but not necessary condition for $a^2<b^2$.  
③ The negation of the proposition "There exists $x \in \mathbb{R}$ such that $x^2+x+1<0$" is: "For all $x \in \mathbb{R}$, $x^2+x+1>0$".  
④ The function $f(x)=\ln x+x- \frac{3}{2}$ has exactly one zero in the interval $(1,2)$.

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