
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
A particle is located at some point on a line. During the first second, it splits in half and the halves move away from each other in opposite directions by a distance of 1 from the original position. During the next second, the resulting particles again split in half and the halves move away from each other in opposite directions by a distance of 1 from their previous positions. When any two particles collide, they annihilate each other. For example, after two seconds, only two particles remain. How many particles will remain after 129 seconds?

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