
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
Starting from $(0,0)$, an object traverses in a coordinate plane by moving in steps of length one either left, right, up, or down, with each direction being equally probable. Determine the probability, denoted as $q$, that the object will reach $(3,2)$ within exactly eight steps. Express $q$ in the form $x/y$, where $x$ and $y$ are coprime positive integers, and calculate $x+y$.

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