
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
Consider a city map resembling an expanded grid where rectangles represent city blocks, and paths between them are streets. $A$, $B$, and $C$ are three intersections. A student walks every morning from $A$ to $B$, only heading east or south and making decisions at each junction to go in either direction with an equal probability of $\frac{1}{2}$. 
Determine the probability that the student passes through intersection $C$ on his route in this extended map where junction $A$ is at the very top-left, $B$ is 4 blocks east and 3 blocks south of $A$, and $C$ is situated 2 blocks east and 1 block south of $A$.
A) $\frac{18}{35}$
B) $\frac{17}{35}$
C) $\frac{1}{2}$
D) $\frac{3}{4}$

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