
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
A piece of paper is flipped upside down, and the digits 0, 1, and 8 remain unchanged when rotated by $180^{\circ}$. The digit 6 becomes 9, and 9 becomes 6. All other digits have no meaning when rotated by $180^{\circ}$. How many 7-digit numbers remain unchanged after being rotated by $180^{\circ}$? Among these, how many are divisible by 4? What is the total sum of these 7-digit numbers that remain unchanged after the rotation by $180^{\circ}$?

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