
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
Euler was the most talented mathematician in the history of science. He invented the formula $e^{ix}=\cos x+i\sin x$, where $i$ is the imaginary unit. By extending the domain of the exponential function to complex numbers, he established the relationship between trigonometric functions and exponential functions. This formula is also known as the "mathematical bridge." According to this formula, the maximum value of $|e^{ix}-2|$ is ____.

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