
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
Let \( AB \) be a focal chord of the parabola \( y^2 = 2px \) (where \( p > 0 \)), and let \( O \) be the origin. Then:
1. The minimum area of triangle \( OAB \) is \( \frac{p^2}{2} \).
2. The tangents at points \( A \) and \( B \) intersect at point \( M \), and the minimum area of triangle \( MAB \) is \( p^2 \).

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