
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 two points, \( A \) and \( O \), circles with variable radius \( r \) are drawn from \( O \). Tangents are drawn from \( A \) to these circles.

(a) Find the maximum area of the isosceles triangle formed by the tangents and the chord of contact.

(b) Find the maximum area of the quadrilateral formed by the tangents and the radii to the points of tangency.

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