
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 at $(0,0)$, an object moves in the coordinate plane with each step being one unit long in any of the four cardinal directions: left, right, up, or down, with equal probability for each direction. Determine the probability, $p$, that the object reaches $(3,1)$ in exactly six steps. Write $p$ in the form $m/n$, where $m$ and $n$ are coprime integers, and find $m+n$.

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