
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  $x_1=1$  and  $x_{n+1} =x_n+\left\lfloor \frac{x_n}{n}\right\rfloor +2$ , for  $n=1,2,3,\ldots $  where  $x$  denotes the largest integer not greater than  $x$ . Determine  $x_{1997}$ .

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