
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
Through the points \( R \) and \( E \), located on the sides \( AB \) and \( AD \) of the parallelogram \( ABCD \), such that \( AR = \frac{2}{3} AB \) and \( AE = \frac{1}{3} AD \), a line is drawn. Find the ratio of the area of the parallelogram to the area of the resulting triangle.

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