
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
Expand the function \( y = x + 1 \) into a Fourier series on the interval \( (0, \pi) \) using the system \( 1, \cos \frac{1}{2} x, \cos \frac{3}{2} x, \ldots, \cos \frac{2n+1}{2} x, \ldots \).

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