
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
The symmetric axis of the parabola $y=a\left(x+h\right)^{2}$ is the line $x=-2$, and it passes through the point $\left(1,-3\right)$.  
$(1)$ Find the analytical expression of the parabola.  
$(2)$ Find the coordinates of the vertex of the parabola.

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