
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 $S_{n}$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$, if $\left(1-2x\right)^{2023}=b_{0}+b_{1}x+b_{2}x^{2}+\cdots +b_{2023}x^{2023}$, where the initial term of the sequence $\{a_{n}\}$ is $a_{1}=\frac{{{b_1}}}{2}+\frac{{{b_2}}}{{{2^2}}}+⋯+\frac{{{b_{2023}}}}{{{2^{2023}}}},{a_{n+1}}={S_n}⋅{S_{n+1}}$, find the value of $S_{2023}$.

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