
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 $xOy$, let $P$ be any point on the curve $C$: $xy=1$ ($x > 0$), and $l$ be the tangent line to the curve $C$ at point $P$, which intersects the coordinate axes at points $A$ and $B$. What is the range of the area of $\triangle OAB$?

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