
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
In trapezoid \(ABCD\), the sides \(AB\) and \(CD\) are parallel and \(CD = 2AB\). Points \(P\) and \(Q\) are chosen on sides \(AD\) and \(BC\), respectively, such that \(DP : PA = 2\) and \(BQ : QC = 3 : 4\). Find the ratio of the areas of quadrilaterals \(ABQP\) and \(CDPQ\).

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