
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
Let \( n \) be a fixed positive integer. Find the sum of all positive integers which have the following properties:
- In their binary representation, they consist of exactly \( 2n \) digits.
- There are exactly \( n \) ones and \( n \) zeros.
- The first digit is not zero.

(Canadian Mathematical Olympiad, 1991)

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