
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
Define a positive integer $n$ as $k$-pretty if $n$ has exactly $k$ positive divisors, $n$ is divisible by $k$, and $n$ is a perfect square. For example, $36$ is $9$-pretty. Let $T$ be the sum of all positive integers less than $1000$ that are $12$-pretty. Calculate $\frac{T}{12}$.

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