
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 circle $M$: $(x)^2+(y-2)^2=1$, $Q$ is a moving point on the $x$-axis, and $QA$ and $QB$ are tangents to the circle $M$ at points $A$ and $B$, respectively.

(1) Find the minimum value of the area of the quadrilateral $QAMB$.
(2) If $|AB|= \frac{4 \sqrt{2}}{3} $, find the equation of line $MQ$.

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