
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
The area of trapezoid \(ABCD\) is 30. Point \(P\) is the midpoint of the lateral side \(AB\). Point \(R\) on side \(CD\) is chosen such that \(2CD = 3RD\). Lines \(AR\) and \(PD\) intersect at point \(Q\). Find the area of triangle \(APQ\) if \(AD = 2BC\).

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