
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
The graph of the quadratic function $y = x^2 + px + q$ passes through the point $(2, -1)$ and intersects the x-axis at two distinct points $A(a, 0)$ and $B(b, 0)$. Let the vertex of the graph be $M$. Find the quadratic function that minimizes the area of $\triangle AMB$.

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