
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
Fill in the table:

| Quadratic Function Properties | Vertex Coordinates | When does $y$ decrease as $x$ increases? |
|-------------------------------|--------------------|----------------------------------------|
| $y=x^{2}+2x+1$                | ______             | ______                                 |
| $y=-\frac{1}{2}x^2+3$         | ______             | ______                                 |
| $y=2\left(x+1\right)\left(x-3\right)$ | ______      | ______                                 |

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