
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 parabola with equation \(y = -\frac{1}{4} x^2 + 5x - 21\) has its vertex at point \(A\) and crosses the \(x\)-axis at \(B(b, 0)\) and \(F(f, 0)\) where \(b < f\). A second parabola with its vertex at \(B\) passes through \(A\) and crosses the \(y\)-axis at \(D\). What are the coordinates of \(D\)?

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