
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 $\cos ( \frac {π}{6}+α) \cdot \cos ( \frac {π}{3}-α)=- \frac {1}{4}$, where $α \in ( \frac {π}{3}, \frac {π}{2})$, find the value of $\sin 2α$ and the value of $\tan α - \frac {1}{\tan α}$.

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