
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  $n$  be a positive integer such that  $\lfloor\sqrt n\rfloor-2$  divides  $n-4$  and  $\lfloor\sqrt n\rfloor+2$  divides  $n+4$ . Find the greatest such  $n$  less than  $1000$ . (Note:  $\lfloor x\rfloor$  refers to the greatest integer less than or equal to  $x$ .)

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