
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  $64$  booths around a circular table and on each one there is a chip. The chips and the corresponding booths are numbered  $1$  to  $64$  in this order. At the center of the table there are  $1996$  light bulbs which are all turned off. Every minute the chips move simultaneously in a circular way (following the numbering sense) as follows: chip  $1$  moves one booth, chip  $2$  moves two booths, etc., so that more than one chip can be in the same booth. At any minute, for each chip sharing a booth with chip  $1$  a bulb is lit. Where is chip  $1$  on the first minute in which all bulbs are lit?

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