
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
The equation of the tangent line to the curve $y=x\ln x$ at $x=e$ is $y=mx+b$, where $m$ is the derivative of $y$ evaluated at $x=e$, and $b$ is the y-coordinate of the point on the curve at $x=e$. Find the equation of this tangent line.

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