
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
On an 8x8 geoboard, points are evenly spaced both vertically and horizontally. Segment $AB$ with a length of 3 units is drawn on this geoboard. After $AB$ is drawn, point $C$ is to be chosen from the remaining 61 points. How many of these points will result in triangle $ABC$ being isosceles?

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