
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 begins its journey on the red dot labelled $A$ on the following lattice. Each minute, the ant moves to an adjacent dot, chosen randomly from its neighbors. Determine the probability that after 7 minutes the ant is at the dot labeled $C$. [asy]
draw((-2,0)--(3,0));
draw((0,-2)--(0,3));
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
draw((1, 0)--(2, 1)--(2, -1));
dot((0, 0)); dot((1, 0)); dot((2, 0)); dot((3, 0)); dot((-1, 0)); dot((-2, 0)); dot((0, 1)); dot((0, 2)); dot((0, 3)); dot((0, -1)); dot((0, -2)); dot((1, 1)); dot((1, -1)); dot((-1, -1)); dot((-1, 1)); dot((2, 1)); dot((2, -1));
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); dot((2,1),blue); dot((2,-1),blue);
label("$A$", (0, 0), SW);
label("$C$", (0, 2), NE);
[/asy]

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