
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  $G$  be the set of points  $(x, y)$  such that  $x$  and  $y$  are positive integers less than or equal to 6.  A *magic grid* is an assignment of an integer to each point in  $G$  such that, for every square with horizontal and vertical sides and all four vertices in  $G$ , the sum of the integers assigned to the four vertices is the same as the corresponding sum for any other such square.  A magic grid is formed so that the product of all 36 integers is the smallest possible value greater than 1.  What is this product?

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