
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 Cartesian coordinate system $xOy$, the graph of the linear function $y=kx+b$ ($kb \neq 0$) passes through the point $(1, kb)$ and intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively. Let the area of $\triangle ABO$ be $S$.
(1) Express $S$ in terms of $b$.
(2) If $b \geq 2$, find the minimum value of $S$.

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