
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 that $a$ and $b$ are positive real numbers, the line $x + y + a = 0$ is tangent to the circle $(x - b)^2 + (y - 1)^2 = 2$. Find the minimum value of $\frac{(3 - 2b)^2}{2a}$.

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