
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 revised magic triangle, each of the six whole numbers from $4$ to $9$ is placed in one of the circles so that the sum, $S$, of three times the top number, twice the numbers on the lower left and lower right, and the numbers on the middle left and middle right of the triangle is the same. Determine the largest possible value for $S$.

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