
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 that a die is rolled twice, let $a$ be the number from the first roll and $b$ be the number from the second roll, determine the probability that the system of equations $ax + by = 3$ and $2x + 4y = 7$ has a unique solution.

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