
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
There are five pairs of integers \((a, b)\) with \(0 \leq a \leq 10\) and \(0 \leq b \leq 10\) for which the points \(P(1,1), Q(4,5)\) and \(R(a, b)\) form a triangle that has area 6. What are these five pairs of integers \((a, b)\)?

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