
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? Select the correct numbers.  
$(1)$ A right triangle has only one altitude.  
$(2)$ An $n$-sided polygon has a total of $n(n-3)$ diagonals.  
$(3)$ Two circles with equal radii are congruent.  
$(4)$ If a polygon has all sides equal, then it is a regular polygon.  
$(5)$ A circle is a set of points in a plane that are equidistant from a fixed point.

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