
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
In the geoboard setup presented, points are spaced evenly in a 6x6 grid format. A line segment $AB$ spans horizontally between points, with $A=(2,2)$ and $B=(5,2)$. Point $C$ is to be selected from the other remaining 23 points. Determine how many of these points allow triangle $ABC$ to be isosceles.

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