
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
Write the Fourier series for the function \( f(x) \) defined by:

$$
\begin{gathered}
f(x)=\left\{\begin{array}{l}
-\frac{\pi}{4},\ -\pi < x < 0 \\
0,\ x = 0,\ x = -\pi \\
\frac{\pi}{4},\ 0 < x < \pi
\end{array}\right. \\
f(x) = f(x + 2\pi).
\end{gathered}
$$

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