
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 the conditions:

$$
\begin{gathered}
f(x)=f(x+2 \pi) \quad (2\pi \text{-periodicity}), \\
f(x)=f(-x) \quad (\text{evenness}) \\
f(x)=x, \quad 0 \leq x \leq \pi.
\end{gathered}
$$

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