
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 $(x+y)^{11}$ 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**) $\frac{1}{2}$
- **B**) $\frac{2}{3}$
- **C**) $\frac{3}{4}$
- **D**) $\frac{5}{6}$
- **E**) $\frac{7}{8}$

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