
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 convex 1994-sided polygon \( M \), 997 diagonals are drawn such that each vertex of \( M \) has exactly one diagonal emanating from it. Each diagonal divides the perimeter of \( M \) into two parts. The number of sides of the smaller part is defined as the length of the diagonal. The lengths of the diagonals are arranged in decreasing order as \((d_{1}, d_{2}, \cdots, d_{997})\). The questions are:

(1) Can the sequence of the diagonal lengths be \((3,3, \cdots, 3, 2, 2, \cdots, 2)\) with 991 threes and 6 twos?

(2) Can the sequence of the diagonal lengths be \((8, \cdots, 8, 6, \cdots, 6, 3, \cdots, 3)\) with 4 eights, 985 sixes, and 8 threes?

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