
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
Let $[x]$ denote the largest integer not greater than the real number $x$. Given the sequence $\left\{a_{n}\right\}$ that satisfies
$$
a_{1}=1, a_{n+1}=1+\frac{1}{a_{n}}+\ln a_{n},
$$
define $S_{n}=\left[a_{1}\right]+\left[a_{2}\right]+\cdots+\left[a_{n}\right]$. Find $S_{n}$.

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