
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 a geoboard where all points are evenly spaced vertically and horizontally, segment $AB$ is of length 3 units and is drawn horizontally. Point $C$ needs to be chosen from the remaining points on a 7x7 grid. How many of the remaining points will result in triangle $ABC$ being isosceles?

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