
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
Given \( p \) and \( q \) are positive numbers such that \( p + 2q = 1 \), evaluate the second and third terms of the binomial expansion of \( (x+y)^{10} \) when evaluated at \( x=p \) and \( y=q \), and set them equal to each other to solve for \( p \).

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