
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
Define: $a$ is a rational number that is not equal to $1$. We call $\frac{1}{1-a}$ the reciprocal difference of $a$. For example, the reciprocal difference of $5$ is $\frac{1}{1-5}=-\frac{1}{4}$, and the reciprocal difference of $-1$ is $\frac{1}{1-(-1)}=\frac{1}{2}$. Given $a_{1}=\frac{1}{2}$, $a_{2}$ is the reciprocal difference of $a_{1}$, $a_{3}$ is the reciprocal difference of $a_{2}$, $a_{4}$ is the reciprocal difference of $a_{3}$, and so on. Find $a_{2023}$.

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