
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  $M$  be the smallest positive multiple of  $2012$  that has  $2012$  divisors. 
Suppose  $M$  can be written as   $\Pi_{k=1}^{n}p_k^{a_k}$  where the  $p_k$ ’s are distinct primes and the  $a_k$ ’s are positive integers. 
Find  $\Sigma_{k=1}^{n}(p_k + a_k)$ 

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