
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
The diagram 12-6 depicts a partial map of a city. Small rectangles represent houses and buildings, while the spaces between them represent streets. A student walks every morning from point $A$ to point $B$ along the streets shown in the diagram, and he can only move either east or south. At each intersection, he has an equal probability, $\frac{1}{2}$, of choosing to move east or south (each choice is independent of other choices). What is the probability that this student passes through point $C$ during his walk?

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