
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 $l_{1}$ and $l_{2}$ are the tangents at two different points $P_{1}$ and $P_{2}$ on the graph of the function $f(x)=|\ln x|$, respectively, and $l_{1}$ and $l_{2}$ intersect the $y$-axis at points $A$ and $B$, respectively. If $l_{1}$ and $l_{2}$ intersect perpendicularly at point $P$, determine the range of the area of $\triangle ABP$.

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