
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
Simplify and evaluate

(Ⅰ) Evaluate \\( \dfrac{ \sqrt{3}\sin (- \dfrac{20}{3}\pi)}{\tan \dfrac{11}{3}\pi}-\cos \dfrac{13}{4}\pi\cdot\tan (- \dfrac{35}{4}\pi) \).

(Ⅱ) Evaluate: \\( \dfrac{\sqrt{1-2\sin {10}^{\circ }\cos {10}^{\circ }}}{\cos {10}^{\circ }-\sqrt{1-{\cos }^{2}{170}^{\circ }}} \)

(Ⅲ) If \\( \sin \theta, \cos \theta \) are the roots of the equation \\( 2{x}^{2}-x+a=0 \) (where \\( a \) is a constant) and \\( \theta \in (0,\pi) \), find the value of \\( \cos \theta - \sin \theta \).

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