
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
Find the minimum value of $\frac{1}{a} + \frac{4}{b}$ if the tangent lines at one of the intersection points of the graphs of the quadratic functions $y = x^2 - 2x + 2$ and $y = -x^2 + ax + b (a > 0, b > 0)$ are perpendicular to each other.

A) $\frac{18}{5}$
B) $\frac{16}{5}$
C) $4$
D) $\frac{24}{5}$

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