
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 that has a minimum value of $-4$ when $x=-1$ and passes through the point $(0,-3)$.  
$(Ⅰ)$ Find the coordinates of the points where the graph of this function intersects the $x$-axis.  
$(Ⅱ)$ Find the maximum value of this function when $-2\leqslant x\leqslant 2$.

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