
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 true one is numbered \_\_\_\_\_\_.  
(1) The negation of the proposition "For all $x>0$, $x^2-x\leq0$" is "There exists an $x>0$ such that $x^2-x>0$."  
(2) If $A>B$, then $\sin A > \sin B$.  
(3) Given a sequence $\{a_n\}$, "The sequence $a_n, a_{n+1}, a_{n+2}$ forms a geometric sequence" is a necessary and sufficient condition for $a_{n+1}^2=a_{n}a_{n+2}$.  
(4) Given the function $f(x)=\lg x+ \frac{1}{\lg x}$, then the minimum value of $f(x)$ is 2.

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