
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
Consider an updated diagram adding vertex G positioned on the line extending from vertex A upwards. The diagram now includes edges connecting A to G and G to D. The task is to find the number of continuous paths from A to B, visiting each labeled point at most once.

[asy]
draw((0,0)--(3,0)--(3,2)--(0,2)--(0,0)--cycle,linewidth(2));
draw((0,2)--(1,0)--(3,2)--(0,2)--cycle,linewidth(2));
draw((0,2)--(1.5,3.5)--(3,2),linewidth(2));
draw((1.5,3.5)--(1.5,5)--(3,2),linewidth(2));

label("$A$",(1.5,5),N);
label("$B$",(0,0),SW);
label("$C$",(0,2),W);
label("$D$",(3,2),E);
label("$E$",(3,0),SE);
label("$F$",(1,0),S);
label("$G$",(1.5,3.5),N);
[/asy]

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