
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
Where is the error in the given equalities?

$$
\begin{aligned}
& \sin x=\frac{e^{i x}-e^{-i x}}{2 i}=\frac{e^{(2 \pi i) \frac{x}{2 \pi}}-e^{(-2 \pi i) \frac{x}{2 \pi}}}{2 i}=\frac{1-1}{2 i}=0 \\
& \cos x=\frac{e^{i x}+e^{-i x}}{2}=\frac{e^{(2 \pi i) \frac{x}{2 \pi}}+e^{(-2 \pi i) \frac{x}{2 \pi}}}{2}=\frac{1+1}{2}=1
\end{aligned}
$$

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