
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
A student walks every morning from intersection $A$ to intersection $B$, only along the streets shown in the diagram, and always heading either north or east. For variety's sake, at each intersection where they can choose a direction, they choose each of the two options with equal probability, $\frac{1}{2}$, independently of previous choices. What is the probability that they will pass through intersection $C$?

![Diagram](https://cdn.mathpix.com/cropped/2024_05_02_e45df204fe230c8b1007g-1.jpg?height=927&width=895&top_left_y=360&top_left_x=607)

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