
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
Mitya, Vanya, and Dima each flipped a coin $2n$ times. It is known that Mitya and Vanya got the same number of heads. What is more likely: event $A$ "Dima got exactly $n$ heads" or event $B$ "Mitya got exactly $n$ heads"? If the events are not equally likely, by what factor is one event more likely than the other?

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