
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 that the domain of the function $f(x)$ is $\mathbf{R}$, and $f(x+2) - 2$ is an odd function, while $f(2x+1)$ is an even function. If $f(1) = 0$, determine the value of $f(1) + f(2) + \cdots + f(2023)$.

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