
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
An expanded grid of a city has intersections labeled A, C, and B. Rectangle blocks are surrounded by streets. The student goes from Home (A) situated at the top left of the grid to School (B) located at the bottom right of a 4x4 block grid. The coffee shop (C) is located such that the student needs to make exactly 3 eastward moves and 2 southward moves from A to C. Calculate the probability that the student, choosing randomly at intersections, will walk through point C on his way to school.

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