
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
Regarding the parabola $y=-3x^{2}$, the following statements are given:<br/>① The parabola opens downwards, and the vertex is at $\left(0,0\right)$;<br/>② The parabola opens upwards, and the vertex is at $\left(0,0\right)$;<br/>③ When $x \lt 0$, $y$ decreases as $x$ increases;<br/>④ When $x \gt 0$, $y$ decreases as $x$ increases;<br/>Among these statements, the correct ones are ______. (Fill in the corresponding numbers)

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