
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

Solve the equation

$$
\operatorname{ctg}\left(2 x(\eta(x+3 \pi)-\eta(x-6 \pi))=\frac{1}{\sin x}-\frac{1}{\cos x}\right.
$$

where $\eta(x)=\left\{\begin{array}{l}1, x \geq 0 \\ 0, x<0\end{array}-\right.$ is the Heaviside function.

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