
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
There are  $k$  piles and there are  $2019$  stones totally. In every move we split a pile into two or remove one pile. Using finite moves we can reach conclusion that there are  $k$  piles left and all of them contain different number of stonws. Find the maximum of  $k$ . 

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