
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
Given a positive integer  $x>1$  with  $n$  divisors, define  $f(x)$  to be the product of the smallest  $\lceil\tfrac{n}{2}\rceil$  divisors of  $x$ . Let  $a$  be the least value of  $x$  such that  $f(x)$  is a multiple of  $X$ , and  $b$  be the least value of  $n$  such that  $f(y)$  is a multiple of  $y$  for some  $y$  that has exactly  $n$  factors. Compute  $a+b$ .

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