
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 point labeled $A$ on a lattice grid at the origin (0, 0). The grid contains dots at all integer coordinate pairs (-2 to 2 both x and y). Each minute, the ant can move up, down, left, or right to another integer coordinate unless blocked by the grid's edge. What is the probability that after 6 minutes he is at the dot labeled $C$ which is at (1,1)?

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