
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
Two hunters, $A$ and $B$, went duck hunting. Assume that each of them hits a duck as often as they miss it. Hunter $A$ encountered 50 ducks during the hunt, while hunter $B$ encountered 51 ducks. What is the probability that hunter $B$'s catch exceeds hunter $A$'s catch?

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