
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 propositions:  
(1) The inverse of a proposition and its negation are not necessarily equivalent;  
(2) If the proposition $P \lor Q$ is true, then $P \land Q$ is also true;  
(3) The hyperbola with asymptotic equations $y = \pm x$ is an equilateral hyperbola (a hyperbola with equal real and imaginary axis lengths);  
(4) The area enclosed by the line $y=1$ and the graph of $y=\cos x$ ($0 \leq x \leq 2\pi$) is exactly the period of the function $y=\cos x$;  
Among these propositions, fill in the correct ones.

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