
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 sequence \( u_{1}, u_{2}, \ldots, u_{n} \) composed of the integers \( 1, 2, \ldots, n \) is quasi-increasing if, for every index \( k \), \( u_{k} \leq u_{k+1} + 2 \). For example, the sequence \( 1, 6, 4, 2, 5, 3 \) is quasi-increasing, but the sequence \( 1, 4, 6, 2, 5, 3 \) is not. Determine the number of quasi-increasing sequences of \( n \) terms.

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