
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
Define a sequence  $\{a_{n}\}_{n=1}^{\infty}$  via  $a_{1} = 1$  and  $a_{n+1} = a_{n} + \lfloor \sqrt{a_{n}} \rfloor$  for all  $n \geq 1$ . What is the smallest  $N$  such that  $a_{N} > 2017$ ?

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