
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 line \(y = \frac{5}{3}x - 15\) crosses the \(x\)-axis at point \(P\) and the \(y\)-axis at point \(Q\). Point \(T(r, s)\) is on segment \(PQ\). If the area of \(\triangle POQ\) is twice the area of \(\triangle TOQ\), what is the value of \(r+s\)?

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