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

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