
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 negligibly small bug starts from the origin of a two-dimensional Cartesian coordinate system. First, it moves 1 unit to the right to the point \((1, 0)\). There, it makes a \(90^\circ\) counterclockwise turn and travels \(\frac{1}{2}\) units, reaching the point \((1, \frac{1}{2})\). If it continues in this manner, making a \(90^\circ\) counterclockwise turn after each segment and traveling half the distance of the previous segment, which point does the bug increasingly approach?

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