
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 three statements:
① The negation of "If $a > b$, then $ac^2 > bc^2$" is a false statement;
② The contrapositive of the statement "If $m > 0$, then the equation $x^2 + x - m = 0$ has real roots" is true;
③ "x + y = 5" is a sufficient but not necessary condition for "$x^2 - y^2 - 3x + 7y = 10$".
Among these statements, the correct ones are numbered as .

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