
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 configuration where points are evenly spaced both vertically and horizontally, segment \( DE \) is drawn using two points, as indicated. Point \( F \) is to be selected from the remaining \( 23 \) points. How many of these \( 23 \) points will result in triangle \( DEF \) being isosceles if \( DE \) is 3 units long? [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((1,2)--(4,2),linewidth(1));
label("D",(1,2),SW);
label("E",(4,2),SE);
[/asy]

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