
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
Find all even natural numbers \( n \) for which the number of divisors (including 1 and \( n \) itself) is equal to \( \frac{n}{2} \). (For example, the number 12 has 6 divisors: \(1, 2, 3, 4, 6, 12\)).

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