
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
(I) Given that $\frac{4\sin \alpha - 2\cos \alpha}{5\cos \alpha + 3\sin \alpha} = \frac{5}{7}$, find the value of $\sin \alpha \cdot \cos \alpha$.

(II) Find the value of $\frac{\sqrt{1 - 2\sin 10^{\circ} \cos 10^{\circ}}}{\cos 10^{\circ} - \sqrt{1 - \cos^{2} 170^{\circ}}}$.

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