
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 that the axis of symmetry of the graph of a quadratic function is $x=-1$, the minimum value of the function is $-4$, and it passes through the point $B(-2,5)$.  
$(1)$ Find the equation of the function.  
$(2)$ Find the coordinates of the points where the graph of the function intersects the coordinate axes.

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