
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
Given a function \( f(x) \) with the domain \( \mathbf{R} \), for any real number \( x \), it holds that \( f(1+x)=f(3-x) \) and \( f(2+x)=-f(1-x) \). Find the value of \( f(1) + f(2) + \cdots + f(100) \).

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