
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 a triangle $\triangle ABC$ with a circumcircle diameter of $1$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given vectors $\overrightarrow{m}=(a,\cos B)$ and $\overrightarrow{n}=(b,\cos A)$, and $\overrightarrow{m}$ is parallel to but not equal to $\overrightarrow{n}$.

1. Find the range of $\sin A+\sin B$.
2. If $abx=a+b$, determine the range of the real number $x$.

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