
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
In a multiplicative magic square, the product of numbers in each row, column, and diagonal must be the same. Consider the square:

$\begin{tabular}{|c|c|c|} \hline 90 & \textit{b} & \textit{c} \\ \hline \textit{d} & \textit{e} & \textit{f} \\ \hline \textit{g} & \textit{h} & 3 \\ \hline \end{tabular}$

If all the entries are positive integers, determine the sum of all possible values for $g$.
A) 3
B) 15
C) 30
D) 45
E) 90

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