
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 that $\sin \theta$ and $\cos \theta$ are the two roots of the equation $x^{2}-2 \sqrt {2}ax+a=0$ with respect to $x$.  
$(1)$ Find the value of the real number $a$;  
$(2)$ If $\theta\in(- \frac {\pi}{2},0)$, find the value of $\sin \theta-\cos \theta$.

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