
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
In triangle $\triangle ABC$, the sides opposite to $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$, respectively. Let vectors $\overrightarrow{m} = (a, \cos B)$ and $\overrightarrow{n} = (b, \cos A)$, and suppose $\overrightarrow{m} \parallel \overrightarrow{n}$ and $\overrightarrow{m} \neq \overrightarrow{n}$.
(I) If $\sin A + \sin B = \frac{\sqrt{6}}{2}$, find the value of $A$;
(II) If the radius of the circumcircle of $\triangle ABC$ is 1, and $abx = a + b$, determine the range of possible values for $x$.

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