
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
Let points \( A \) and \( B \) be on the graph of the function \( f(x) = 3 - x^2 \) and lie on opposite sides of the \( y \)-axis. Find the minimum area of the region enclosed by the tangents to \( f(x) \) at points \( A \) and \( B \) and the \( x \)-axis.

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