
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 \( f(x) \), where

\[
\begin{gathered}
f(x)=\left\{\begin{array}{l}
x, \quad |x|<\pi \\
0, \quad x=-\pi
\end{array}\right. \\
f(x)=f(x+2 \pi)
\end{gathered}
\]

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