
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
An ant starts at the dot labeled $C$ and moves in the following lattice. Each minute, the ant moves to one of the neighboring dots (including diagonally neighboring dots, if any). What is the probability that after 6 minutes the ant is at the dot labeled $D$?
[asy]
draw((-2,0)--(2,0));
draw((0,-2)--(0,2));
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
draw((-1,0)--(-1,1)--(0,2)--(1,1)--(1,0)--(1,-1)--(0,-2)--(-1,-1)--cycle);
dot((0,0)); dot((1,0)); dot((2,0)); dot((-1,0)); dot((-2,0));
dot((0,1)); dot((0,2)); dot((0,-1)); dot((0,-2)); dot((1,1)); dot((1,-1)); dot((-1,-1)); dot((-1,1));
label("$C$",(-1,-1),S);
label("$D$",(1,1),N);
[/asy]

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