
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 \( K = 6 \). This number has 4 divisors, so \( L = 4 \). The number 4 has 3 divisors, which is exactly \( \frac{K}{2} \). This also fits.

So, it turns out that there are two possibilities: \( K=4, L=3 \), and \( K=6, L=4 \). In the first case, the sum \( K + 2L \) equals 10, and in the second case, it equals 14. But both 10 and 14 have the same number of divisors, which is 4.

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