
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]


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Let \( E \) be the set of \( 1983^{3} \) points of the space \( \mathbb{R}^{3} \), all three of whose coordinates are integers between 0 and 1982 (including 0 and 1982). A coloring of \( E \) is a map from \( E \) to the set \(\{\text{red}, \text{blue}\}\). How many colorings of \( E \) are there satisfying the following property: The number of red vertices among the 8 vertices of any right-angled parallelepiped is a multiple of 4?

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