
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
There is a military exercise where a defensive line has 20 posts. To test 5 different new weapons, it is planned to equip 5 posts with these new weapons. The first and last posts must not be equipped with new weapons, and at least one of every five consecutive posts must be equipped with a new weapon. Also, no two adjacent posts should both be equipped with new weapons. How many different ways are there to equip the posts with new weapons? (2005 Zhejiang Province Preliminary Exam Question)

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