
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
Given the shape in the bottom right diagram, if we fill each of the 16 squares with the numbers 1, 3, 5, and 7, such that each row and each column contains all different numbers, and the four numbers in each tile also contain no repetitions, calculate the average number in the four squares marked $A, B, C,$ and $D$.

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