
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
In the Cartesian coordinate system $xOy$, $P$ is a point on the curve $C$: $y=e^{x}$, and the line $l$: $x+2y+c=0$ passes through point $P$ and is perpendicular to the tangent line of curve $C$ at point $P$. Find the value of the real number $c$.

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