
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 $A$ on a lattice where each dot is either red or blue. The ant moves randomly every minute to an adjacent dot. Determine the probability that after 7 minutes the ant ends up at dot labeled $C$. Assume the lattice layout and dot colors as follows:
[asy]
draw((-2,0)--(3,0));
draw((0,-2)--(0,3));
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
dot((0,0), red); dot((1,0), blue); dot((2,0), red); dot((3,0), blue); dot((-1,0), blue); dot((-2,0), red); dot((0,1), blue); dot((0,2), red); dot((0,3), blue); dot((0,-1), blue); dot((0,-2), red); dot((1,1), red); dot((1,-1), red); dot((-1,-1), red); dot((-1,1), red);
label("$A$",(0,0),SW);
label("$C$",(1,0),NE);
[/asy]

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