
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 math teacher proposed changing the voting scheme for a play contest. According to her, a jury of $2m$ people $(2m \leq n)$ should be randomly selected from all $2n$ moms. Find the probability that the best play will win under these voting conditions.

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