
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
It is known that the graph of a quadratic function is symmetric with respect to the y-axis, and passes through the points (0, -2) and (1, -1).
(1) Determine the equation of this quadratic function.
(2) Determine the number of points of intersection between the graph of the quadratic function and the x-axis.

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