
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, __________ is true.  
① The negation of "For all $x \in \mathbb{R}, x^2+1>1$" is "$x \in \mathbb{R}, x^2+1\leq1$";  
② The contrapositive of "If $x^2+y^2=0$, then both $x$ and $y$ are $0$";  
③ The converse of "If $\{a_n\}$ is a geometric sequence, then $a_n=a_1 \times q^{n-1}$";  
④ The negation of "If $\sin a + \cos a = (0<a<\pi)$, then $a$ is an acute angle".

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