
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 expanded geoboard shown, points are placed evenly in a $6\times6$ grid. Segment $AB$ is drawn horizontally using two points (B,C) spaced three units apart. From the remaining $34$ points, how many choices are there for a point $D$ such that triangle $ABD$ is isosceles? [asy]
draw((0,0)--(0,7)--(7,7)--(7,0)--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