
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
There are the following propositions:  
(1) A parallelepiped with 2 rectangular faces is a right prism.  
(2) A solid of revolution generated by rotating a right-angled triangle about one of its legs is necessarily a cone.  
(3) If a line is parallel to a line within a plane, then this line must be parallel to that plane.  
(4) There exist two skew lines $a$ and $b$, with $a \subset \alpha$, $b \subset \beta$, $a \parallel \beta$, $b \parallel \alpha$.  
The correct propositions are:

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