
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 $a_{1}=1$, $a_{n+1}=\ln a_{n}+2$, and let $T_{n}=\sum_{i=1}^{n}[a_{i}]$ (where $\left[x\right]$ represents the greatest integer not exceeding $x$, for example, $\left[-0.5\right]=-1$, $\left[2\right]=2$), find $T_{2023}$.

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