
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 the function $f(x)=x- \frac {lnx}{ax}(a≠0)$, the tangent line $l_1$ at the point (1, f(1)) and the tangent line $l_2$ at the point (e, f(e)) are perpendicular to each other. Find the coordinates of the intersection point of $l_1$ and $l_2$.

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