
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
Six identical rectangles are arranged to form a larger rectangle $PQRS$, and the area of $PQRS$ is $6000$ square units. The three rows of rectangles form $PQ$ while two columns form $PS$. What is the length, $x$, rounded off to the nearest integer, if one side of each rectangle is $x$ and the other is $\frac{2}{3}x$?

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