
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
\( ABCDEFGH \) is a cube in which \(ABCD\) is the top face, with vertices \(H\), \(G\), \(F\), and \(E\) directly below the vertices \(A\), \(B\), \(C\), and \(D\) respectively. A real number is assigned to each vertex. At each vertex, the average of the numbers in the three adjacent vertices is then computed. The averages obtained at \(A, B, C, D, E, F, G, H\) are 1, 2, 3, 4, 5, 6, 7, 8 respectively. Find the number assigned to vertex \(F\).

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