
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 each one of the given  $2019$  boxes, there are  $2019$  stones numbered as  $1,2,...,2019$  with total mass of  $1$  kilogram. In all situations satisfying these conditions, if one can pick stones from different boxes with different numbers, with total mass of at least 1 kilogram, in  $k$  different ways, what is the maximal of  $k$ ?

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