
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]


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In a coordinate plane, four lines are drawn by the equations \( 3x + 4y - 12 = 0 \), \( 5x - 4y - 10 = 0 \), \( x = 3 \), and \( y = 1 \). Calculate the area of the quadrilateral formed by the intersection of these lines.

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