
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 the parabola \( C: x^{2} = 2py \) with \( p > 0 \), two tangents \( RA \) and \( RB \) are drawn from the point \( R(1, -1) \) to the parabola \( C \). The points of tangency are \( A \) and \( B \). Find the minimum area of the triangle \( \triangle RAB \) as \( p \) varies.

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