
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 parabola is defined by the equation x²=4y. Two tangent lines, HA and HB, are drawn from point H(1, -1) to the parabola, intersecting it at points A and B. Calculate the area of triangle ABH.

A) $$\frac {5 \sqrt {5}}{4}$$
B) $$\frac {5 \sqrt {5}}{2}$$
C) $$\frac {3 \sqrt {5}}{2}$$
D) $$5 \sqrt {5}$$

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