
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 $f(x)=e^{2x}-2e^{x}+2x$ and the tangent line equation $l:y=g(x)$ at point $P(x_{0}, f(x_{0}))$. If for any $x\in \mathbb{R}$, $(x-x_{0})(f(x)-g(x))\geqslant 0$ holds, then $x_{0}=\_\_\_\_\_\_$.

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