
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
In a larger section of the same city map, a student needs to walk from intersection $A$ to intersection $B$, passing through intersections $C$ and $D$ en route. The student starts at $A$ and can only travel east or south along the streets. Each morning, the decisions at intersections to go east versus south are influenced by a weighted coin, with a $\frac{2}{3}$ chance of going east and a $\frac{1}{3}$ chance of going south. Determine the probability that the student passes through $C$ and then $D$ on his way from $A$ to $B$.
A) $\frac{1}{126}$
B) $\frac{8}{945}$
C) $\frac{8}{1890}$
D) $\frac{8}{210}$
E) $\frac{4}{945}$

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