
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 rearranged city grid, a student walks from intersection A to intersection B, always heading either east or south. The student starts his walk each day aiming for intersection B but this time aims to pass through a specific point D. The grid structure requires 1 eastward and 3 southward moves to reach D from A. From D to B, the student needs 2 eastward and 1 southward move. Calculate the probability that the student passes through D on his journey, given that he randomly chooses his direction at each intersection with equal likelihood.
A) $\frac{11}{32}$
B) $\frac{12}{35}$
C) $\frac{15}{34}$
D) $\frac{21}{32}$
E) $\frac{3}{4}$

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