
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
Triangle \( PQR \) has vertices at \( P(4, 9) \), \( Q(2, -3) \), and \( R(7, 2) \). The point \( S \) with coordinates \( (x, y) \) is chosen inside the triangle so that the three smaller triangles \( PQS \), \( PRS \), and \( QRS \) all have equal areas. What is the value of \( 8x + y \)?

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