
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
Mady has an infinite number of balls and empty boxes that can each hold five balls. The empty boxes are organized in a row, each capable of holding one more ball than in the previous problem (now up to five balls). At each step, Mady places a ball in the first box of the row that has room and empties any boxes to its left if they were full and the addition causes a carryover in the senary (base-6) numbering system. How many balls will be in the boxes after Mady's $2010$th step?

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