
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
Consider the function \( f(x) \) defined by the conditions:

\[
\begin{gathered}
f(x) = f(x + 2\pi) \quad (\text{periodicity of } 2\pi) \\
f(x) = -f(-x) \quad (\text{oddity}) \\
f(x) = \pi - x, \quad 0 < x \leqslant \pi, \quad f(0) = 0
\end{gathered}
\]

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