
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 polynomial \((x+y)^{10}\) is expanded in decreasing powers of x. The third and fourth terms have equal values when evaluated at \(x = p\) and \(y = q\), where \(p\) and \(q\) are positive numbers whose sum is two. What is the value of \(p\)?
**A)** \( \frac{15}{11} \)  
**B)** \( \frac{16}{11} \)  
**C)** \( \frac{17}{11} \)  
**D)** \( \frac{18}{11} \)

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