
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
The graph of the function $y=f(x)$ defined on $R$ is symmetric with respect to the point $({-\frac{3}{4},0})$. For any real number $x$, it holds that $f(x)=-f({x+\frac{3}{2}})$, and $f(-1)=1$, $f(0)=-2$. Determine the value of $f(1)+f(2)+f(3)+\cdots +f(2024)$.

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