
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
A point M is situated on the parabola C described by $y^2 = 2px$ ($p > 0$). Perpendicular lines are drawn from M to the directrix of C and to the x-axis, forming a square with side length 4 alongside the directrix of C and the x-axis, with point M in the first quadrant.
(1) Determine the equation of the parabola C and the coordinates of point M;
(2) Two lines that are equally inclined to the axis make up angle bisectors through point M, intersecting the parabola C at points A and B, respectively, and the straight line AB passes through point (0, -1). Compute the area of triangle $\triangle MAB$.

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