
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 sequence $\{a_{n}\}$, where $a_{1}=1$, $a_{2}=2$, and $a_{n+2}-3 a_{n+1}+2 a_{n}=1$. Let $T_{n}$ be the sum of the first $n$ terms of the sequence $\left\{\frac{8}{a_{n}}\right\}$. Then, find $\left[T_{2023}\right]$. (The symbol $[x]$ denotes the greatest integer less than or equal to $x$)

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