
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

By transforming the equation, we get $\left(\sin x - \frac{1}{\sin x}\right)^{2} = \cos x \left(\sin x - \frac{1}{\sin x}\right)$. Hence, either $\sin x - \frac{1}{\sin x} = 0$ or $\sin x - \frac{1}{\sin x} = \cos x$. Therefore, $\cos x = 0$, i.e., $x = \pi / 2 + \pi k, k \in \mathbb{Z}$. From the second equation, we find that either $\cos x = 0$ or $\tan x = -1$. Consequently, $x = -\pi / 4 + \pi m$.

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