
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
In the plane Cartesian coordinate system $xOy$, it is known that point $A\left(-1, y_{0}\right)$ and point $B(2,0)$ are on the parabola $y = ax^2 + bx \ (a > 0)$. The area of $\triangle AOB$ is equal to 1.
1. Find the equation of the parabola.
2. The equation of the line $l$ is $y = x - \frac{25}{4}$. Point $P$ is any point on the parabola. Find the minimum distance from point $P$ to the line $l$ and the coordinates of point $P$ when this minimum distance occurs.

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