
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 curvilinear trapezoid is enclosed by the curve $y=e^x$, the line $y=0$, and the vertical lines $x=1$ and $x=5$. A tangent line is drawn to the curve $y=e^x$ at a point $P$ within the interval $x\in[1,5]$. This tangent line cuts a common trapezoid with the maximum area from the curvilinear trapezoid. Find the coordinates of point P.

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