
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 the line $l\_1$: $x-2y-1=0$, and the line $l\_2$: $ax+2y+2a=0$, where $a$ is a real number and $a∈[-1,5]$. Calculate the probability that the intersection point of lines $l\_1$ and $l\_2$ lies in the first quadrant.

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