
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 shown, points are placed in a uniform grid within a square boundary. Segment $AB$ is drawn on the geoboard, where $A$ and $B$ are both on the horizontal line with a horizontal distance of three grid units between them. Choose point $C$ from the remaining points. How many of these points will result in an isosceles triangle $ABC$? Assume there are 20 other points available on the geoboard. [asy]
draw((0,0)--(0,5)--(5,5)--(5,0)--cycle,linewidth(1));
for(int i=1;i<5;++i)
{for(int j=1;j<5;++j)
{dot((i,j));}
}
draw((1,2)--(4,2),linewidth(1));
label("A",(1,2),SW);
label("B",(4,2),SE);
[/asy]

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