
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
Which of the following statements are correct?

(1) The condition for vertical angles to be equal is that there are two angles that are vertical angles.  
(2) The converse of "all right angles are equal" is "angles that are equal are right angles".  
(3) A common factor of $a^2-4$ and $a^2-4a+4$ is $a-2$.  
(4) Two triangles are congruent if one angle and the two sides adjacent to that angle are respectively equal.  
(5) $(a^2-2)^2=a^4-4$.

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