
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 a quadratic function $y=ax^2+bx+c$ (where $a>0$, $b>0$) whose graph passes through the points $(0, y_1)$, $(1, y_2)$, and $(-1, y_3)$, and satisfies $y_1^2=y_2^2=y_3^2=1$, find the explicit formula for this quadratic function.

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