
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 $3 \times 3$ square grid, the numbers $1, 2, 3, \ldots, 9$ are placed. Then, in each circle (Fig. 2), the arithmetic mean of the four surrounding numbers is recorded. After that, the arithmetic mean of these four resulting numbers is calculated. What is the largest number that can be obtained?

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