
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
Points \( P \) and \( Q \) are located on side \( BC \) of triangle \( ABC \), with \( BP: PQ: QC = 1: 2: 3 \). Point \( R \) divides side \( AC \) of this triangle such that \( AR: RC = 1: 2 \). What is the ratio of the area of quadrilateral \( PQST \) to the area of triangle \( ABC \), if \( S \) and \( T \) are the intersection points of line \( BR \) with lines \( AQ \) and \( AP \), respectively?

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