
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 100 light bulbs arranged in a row on a Christmas tree. The bulbs are then toggled according to the following algorithm: initially, all the bulbs are turned on; after one second, every second bulb is turned off; after another second, every third bulb is toggled (turned off if it was on, turned on if it was off); after another second, every fourth bulb is toggled, and so on. After 100 seconds, the process stops. Find the probability that a randomly selected bulb is on after this process (the bulbs do not burn out or break).

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