
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
Call a \(2n\)-digit base-10 number special if we can split its digits into two sets of size \(n\) such that the sum of the numbers in the two sets is the same. Let \(p_{n}\) be the probability that a randomly-chosen \(2n\)-digit number is special. (We allow leading zeros in \(2n\)-digit numbers). The sequence \(p_{n}\) converges to a constant \(c\). Find \(c\).

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