
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) In certain rural areas of Russia, there was a fortune-telling tradition. A girl would hold six blades of grass in her hand so that the ends of the blades would stick out from the top and bottom. Her friend would then tie these blades of grass in pairs from the top and bottom separately. If all six blades of grass were tied into a single ring, it was supposed to mean that the girl would get married within the year. What is the probability that the blades of grass will form a single ring when tied randomly?

b) Solve the same question for the case of $2n$ blades of grass.

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