
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

$$
\cos \left(2 x \left(\eta(x+3 \pi)-\eta(x-8 \pi)\right)\right) = \sin x + \cos x
$$

where $\eta(x)$ is the Heaviside function defined by

$$
\eta(x)=\begin{cases}
1, & x \geq 0 \\
0, & x < 0
\end{cases}
$$.

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