
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
On the number line, the rational number $a$ and $\frac{1}{1-a}$ are represented by points $A$ and $A_{1}$, respectively. We call point $A_{1}$ the "reciprocal difference point" of point $A$. It is known that the reciprocal difference point of point $A$ is point $A_{1}$, the reciprocal difference point of point $A_{1}$ is point $A_{2}$, and so on. If the rational numbers represented by points $A$, $A_{1}$, $A_{2}$, $A_{3}$, $\ldots A_{n}$ on the number line are $a$, $a_{1}$, $a_{2}$, $a_{3}$, $\ldots a_{n}$, then when $a=\frac{1}{2}$, the value of the algebraic expression $a_{1}+a_{2}+a_{3}+a_{4}+\cdots +a_{2023}$ is ______.

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