
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 below, the points are evenly spaced vertically and horizontally. Segment $AB$ is drawn using two points, as shown. Point $C$ is to be chosen from the remaining $48$ points. How many of these $48$ points will result in triangle $ABC$ being isosceles? 
```plaintext
[asy]
draw((0,0)--(0,8)--(8,8)--(8,0)--cycle,linewidth(1));
for(int i=1;i<7;++i)
{for(int j=1;j<7;++j)
{dot((i,j));}
}
draw((2,2)--(5,2),linewidth(1));
label("A",(2,2),SW);
label("B",(5,2),SE);
[/asy]
```

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