
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 die is thrown twice. Let $a$ be the number that appears on the first throw and $b$ be the number that appears on the second throw. Consider two lines $l_{1}: ax + by = 2$ and $l_{2}: x + 2y = 2$. Compute the value of $p_{2} - p_{1}$, where $p_{1}$ is the probability that $l_{1}$ and $l_{2}$ are parallel and $p_{2}$ is the probability that they intersect.

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