
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 a quadratic function $y=x^{2}+bx+c$, its graph passes through the intersection points of the graph of the function $y=-3x+3$ and the $x$-axis, $y$-axis. Find the analytical expression of this quadratic function and directly answer whether this function has a maximum or minimum value, and its value.

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