
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 graph of the quadratic function $y=-x^{2}+2x+1$ is a parabola $C$.  
$(1)$ Write down the direction of the opening of the parabola $C$, its axis of symmetry, and the coordinates of the vertex.  
$(2)$ When $0\leqslant x\leqslant 3$, find the range of the function values $y$ of this quadratic function.

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