
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
Choose a point \( P \) on the line \( x = 3 \) and draw two tangents from \( P \) to the circle \( x^2 + (y - 2)^2 = 4 \) which touch the circle at points \( A \) and \( B \). Then, the line \( AB \) passes through a fixed point. Find the coordinates of this fixed point.

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