
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 $P$ has dimensions $2a$ and $3a$ where $a>0$. Find how many rectangles with dimensions $x$ and $y$ satisfy $x, y < 2a$ such that the perimeter of the new rectangle is two-thirds that of $P$, and the area is two-ninths that of $P$.
A) 0
B) 1
C) 2
D) 3
E) 4

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