
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 the permutation \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) of \(1, 2, 3, 4, 5\), how many permutations are there that satisfy \(a_{1} < a_{2}, a_{2} > a_{3}, a_{3} < a_{4}, a_{4} > a_{5}\)?

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