
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 a dot labeled $A$ on a similar lattice as previously described. Every minute, the ant can either move to one of its neighboring dots or decide to stay at its current position, doing each with equal likelihood. What is the probability that after 7 minutes he ends up at the dot labeled $C$? Assume $C$ is a new label for the red dot (0,2).

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