
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
In the sequence \( \left\{a_{n}\right\}_{n=1}^{+\infty} \), where \( x_{1}=1 \), for any positive integer \( n \), \( x_{n+1}=x_{n}+\left[\sqrt{x_{n}}\right] \), where the symbol \( [x] \) denotes the greatest integer not exceeding \( x \), find the smallest positive integer \( n \) such that \( x_{n} \geqslant 2019 \).

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