
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
Verify that the product \((a+b \sqrt{5})(c+d \sqrt{5})\) can again be represented in the form \(p+q \sqrt{5}\). Ensure that if \(a \geq 0, b \geq 0, c \geq 0, d \geq 0\), then \(p \geq 0\) and \(q \geq 0\) as well.

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