
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 \( P(2, 5) \), \( Q(-1, -3) \), and \( R(7, 0) \). A point \( S \) with coordinates \( (x, y) \) is placed inside the triangle so that the areas of triangles \( PQS \), \( PRS \), and \( QRS \) are equal. Determine the value of \( 7x + 3y \).

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