
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 the $7 \times 7$ grid shown in the diagram, each cell must be filled with a number such that all cells with the same number are connected to each other (two connected cells must share a common edge). The numbers 1, 2, 3, 4, and 5 have already been placed, each appearing twice. Calculate the sum of all the numbers in the grid.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline 1 & & & & & & 2 \\
\hline 5 & 3 & & & 3 & 4 & \\
\hline & & & 2 & & & \\
\hline & & & & & & \\
\hline & & & & 1 & & \\
\hline & & 5 & & & & \\
\hline 4 & & & & & & \\
\hline
\end{tabular}

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