
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 small ant starts at the origin on a coordinate plane. It first moves two units to the right, reaching (2, 0). Then, it turns $90^\circ$ clockwise and moves one unit down. If it continues in this pattern, making a $90^\circ$ clockwise turn each time and traveling half the distance of the previous move, determine the point it will get closest to.

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