
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 one. What is the value of \( p \)?
**A)** $\frac{3}{8}$  
**B)** $\frac{5}{8}$  
**C)** $\frac{8}{11}$  
**D)** $\frac{7}{10}$  
**E)** $\frac{9}{12}$

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