
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
Let \( Q \) be the set of some permutations of the numbers \( 1, 2, \ldots, 100 \) such that for any \( 1 \leq a, b \leq 100 \) with \( a \neq b \), there is at most one \( \sigma \in Q \) where \( b \) immediately follows \( a \) in \( \sigma \). Find the maximum number of elements in the set \( Q \).

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