
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 points A(1, 4), B(3, 2), and C(1, 1).
(Ⅰ) Find the equation of the line that passes through point C and is parallel to line AB;
(Ⅱ) If the perpendicular bisector of segment AB intersects the x-axis and y-axis at points M and N, respectively, find the area of triangle OMN.

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