
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 the sequence  $a_i$  as follows:  $a_1 = 1, a_2 = 2015$ , and  $a_n = \frac{na_{n-1}^2}{a_{n-1}+na_{n-2}}$  for  $n > 2$ . What is the least  $k$  such that  $a_k < a_{k-1}$ ?


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