
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
A line \( l \) passing through the origin \( O \) intersects the graph of the function \( f(x) = |\ln x| \) (where \( x \) is in the interval \( (0, e) \) with \( e \) being the base of natural logarithms) at points \( A \) and \( B \), from left to right. If point \( A \) is the midpoint of \( OB \), find the coordinates of point \( A \).

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