
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 the quadratic function $y=-2{x}^{2}+6x-\frac{1}{2}$,

(1) State the direction in which the graph opens, the equation of the axis of symmetry, and the coordinates of the vertex;

(2) Explain how the graph of the function can be obtained by transforming the graph of $y=-2{x}^{2}$;

(3) Find the range of the function on the interval $[0,2]$.

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