
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 a geoboard with points evenly spaced vertically and horizontally, segment $DE$ is drawn using two points, as shown. Point $F$ is to be chosen from the remaining $23$ points. How many of these $23$ points will result in triangle $DEF$ being isosceles if $DE = 3$ units? Assume $DE$ is horizontal. [asy]
draw((0,0)--(0,6)--(6,6)--(6,0)--cycle,linewidth(1));
for(int i=1;i<6;++i)
{for(int j=1;j<6;++j)
{dot((i,j));}
}
draw((2,2)--(5,2),linewidth(1));
label("D",(2,2),SW);
label("E",(5,2),SE);
[/asy]

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