
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
The line \(2y + (x + 4) = 2a\) intersects the line \(-x + y = 3\) at the point with abscissa \(x = \frac{2a - 10}{3}\). Considering that \(x \in [-3, 0]\), this occurs when \(a \in \left[\frac{1}{2}, 5\right]\). The line \(2y + (x + 4) = 2a\) intersects the line \(x + y = 3\) at the point with abscissa \(x = 10 - 2a\). Considering that \(x \in [0, 3]\), this occurs when \(a \in \left[\frac{7}{2}, 5\right]\). Consequently, the system has two solutions when \(a \in \left[\frac{7}{2}, 5\right)\). The probability of this event, assuming a uniform distribution, equals the ratio of the length of the segment \(\left[\frac{7}{2}, 5\right]\) to the length of the segment \([-1, 5]\), i.e., \(P(A) = \frac{1}{4}\).

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