
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
A polynomial $(x+y)^8$ is expanded decreasingly in powers of $x$. The third and fourth terms are equal when $x=a$ and $y=b$, where $a$ and $b$ are positive numbers such that their product is half. What is the value of $a$?
**A)** 0.5
**B)** 1
**C)** 1.5
**D)** 2

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