
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
The prime numbers 2, 3, 5, 7, 11, 13, and 17 are arranged in a multiplication table, with three along the top and the other four down the left. The multiplication table is completed and the sum of the twelve entries is tabulated. What is the largest possible sum of the twelve entries given that the number 17 must be in the top row?

\[
\begin{array}{c||c|c|c|}
\times & a & b & c \\ \hline \hline
d & & & \\ \hline
e & & & \\ \hline
f & & & \\ \hline
g & & & \\ \hline
\end{array}
\]

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