
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
Given a modified lattice, an ant starts at the dot labeled $A$ and aims to reach a dot labeled $C$ in 6 minutes. The ant can move as follows: it begins at the red dot labeled $A$ and can move to any adjacent blue dot in 1 minute; then it must move to a nearby red dot in the next minute. After 4 movements, a specific dot $E$ (a blue dot) becomes unavailable for the remainder of the time. Calculate the probability that after 6 minutes the ant is at the dot labeled $C$. The diagram is structured as follows:
- A central red dot $A$, surrounded by four blue dots: north, south, east, west.
- Each blue dot further connects to one red dot (not $A$) in the respective direction.
- Dot $E$ is the blue dot to the north of $A$.
- Dot $C$ is one of the red dots, specifically the one to the northeast of $A$.

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