
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 2021 light bulbs in a row, labeled 1 through 2021, each with an on/off switch.  They all start in the off position when 1011 people walk by.  The first person flips the switch on every bulb; the second person flips the switch on every 3rd bulb (bulbs 3, 6, etc.); the third person flips the switch on every 5th bulb; and so on.  In general, the  $k$ th person flips the switch on every  $(2k - 1)$ th light bulb, starting with bulb  $2k - 1$ .  After all 1011 people have gone by, how many light bulbs are on?

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