
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 $\frac {4\sin\alpha-2\cos\alpha}{5\cos\alpha +3\sin\alpha } = \frac {5}{7}$, find the value of $\sin\alpha \cdot \cos\alpha$;
(Ⅱ) Calculate 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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