
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 \( y = f(x) \) with its vertex at \((-1, 1)\) and its y-intercept at \((0, 2)\):

1. Find the expression of the quadratic function.
2. When \( x = 8 \), what is the value of \( y \)?
3. For any given value of \( y \), can we always find a corresponding value of \( x \)? Why? Provide an explanation using the graph.

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