
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
Select an even number $a$ and an odd number $b$ from the set $\{1, 2, 3, 4\}$ to form a vector $\boldsymbol{\alpha} = (a, b)$ with the origin as the starting point. Among all such vectors originating from the origin, two vectors are randomly chosen to form adjacent sides of a triangle. The probability that the resulting triangle has an area of 1 is ( ).

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