
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
Find the number of different permutations of five distinct elements \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) with the following restrictions:
- \(a_{1}\) does not occupy the 1st or 2nd position,
- \(a_{2}\) does not occupy the 2nd or 3rd position,
- \(a_{3}\) does not occupy the 5th position,
- \(a_{4}\) does not occupy the 4th or 5th position,
- \(a_{5}\) does not occupy the 3rd or 4th position. 

How many different permutations can be made?

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