
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
Write down a quadratic function whose graph satisfies the following conditions: ① opens downward; ② intersects the $y$-axis at the point $\left(0,3\right)$. The analytical expression of this quadratic function can be ____.

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