
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 $a \gt 0$, $S_1=\frac{1}{a}$, $S_2=-S_1-1$, $S_3=\frac{1}{S_2}$, $S_4=-S_3-1$, $S_5=\frac{1}{S_4} \ldots$ (i.e., when $n$ is an odd number greater than $1$, $S_n=\frac{1}{S_{n-1}}$; when $n$ is an even number greater than $1$, $S_{n}=-S_{n-1}-1$). Following this pattern, when $a=2$, $S_{2023}=\_\_\_\_\_\_$.

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