
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
Assume we have  $95$  boxes and  $19$  balls distributed in these boxes in an arbitrary manner. We take  $6$  new balls at a time and place them in  $6$  of the boxes, one ball in each of the six. Can we, by repeating this process a suitable number of times, achieve a situation in which each of the  $95$  boxes contains an equal number of balls?

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