
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's formula $e^{xi}=\cos x+i\sin x(i$ is an important discovery made by the famous Swiss mathematician Euler. It extends the domain of the exponential function to complex numbers, establishes the relationship between trigonometric functions and exponential functions, and is known as the "mathematical bridge." According to this formula, $|e^{xi}|=$______, $e^{xi}+e^{-xi}=\_\_\_\_\_\_$.

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