
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
A rectangle $ABCD$ has sides $AB = 3$, $CD = AD$, and $BC = x$, where $x$ and $CD$ are positive integers. The perimeter of rectangle $ABCD$ is less than 1000. How many different values of the perimeter $p$ are possible?

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