
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 circle $O: x^2 + y^2 = 4$ and the point $M(1, a)$.
- (I) If there is exactly one line passing through point $M$ that is tangent to circle $O$, find the value of the real number $a$ and the equation of the tangent line.
- (II) If $a = \sqrt{2}$, and through point $M$ there are two chords $AC$ and $BD$ of circle $O$ that are perpendicular to each other, find the maximum value of $|AC| + |BD|$.

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