
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 a point P(1, a) and a circle $x^2+y^2=4$.
(1) If there is only one tangent line to the circle passing through point P, find the value of a and the equation of the tangent line;
(2) If $a=\sqrt{2}$, and two chords AC, BD passing through point P are perpendicular to each other, find the maximum area of quadrilateral ABCD.

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