
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 \( a_{i} = 0,1 \) for \( i = 1, 2, \cdots, n \). Find the number of sequences \(\left(a_{1}, a_{2}, \cdots, a_{n}\right)\) that satisfy \( a_{1} \leqslant a_{2}, a_{2} \geqslant a_{3}, a_{3} \leqslant a_{4}, a_{4} \geqslant a_{5}, \cdots \).

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